Senator Leroy Clark takes a charter jet across the country to an empty stretch of desert. The plane taxis to a halt in the middle of nowhere. A car pulls up as the plane departs and Clark gets in. As they drive across the desert, the passenger, Dr. Doug Phillips, calls ahead to Project Tic-Toc and gets permission to enter. A huge door opens up in the desert and the car drives into it and out of sight as the door closes behind it.
Deep within the earth, the car pulls to a stop at the end of a Tunnel and Doug gets out. He escorts Clark past armed guards and introduces him to Master Sgt. Jiggs, the head of their security force. Jiggs takes their briefcases and Doug takes Clark across a walkway over a vast underground chamber. He explains that each of the three complexes holds 12,000 people each, and each complex has 800 floors. Clark says that he wonders if time travel is really worth all of the expense and Doug insists that it's the most valuable treasure of all.
The two men continue to a chamber and drop 800 floors via elevator. Lt. General Haywood Kirk greets them and welcomes his old friend Clark. The two of them served together and are on good terms, and Kirk realizes that Clark is there to investigate the expenditures. He shows off the complex around them and Doug suggests that Tony should be there. They go to the control chamber that contains the central piece of equipment for the entire compound: the Time Tunnel. The structure is made up of a series of metal concentric circles extending into infinity.
As he examines the Tunnel, Clark points out that they have only conducted experiments with animals, and they have never brought back any of their subjects. Clark points out that he's only speculating and the whole project costs $7 billion. Doug calls to Tony, a young scientist, who emerges from the Tunnel. Doug assures Clark that Tony is competent despite his age. When Clark says that he's there to investigate whether the project works, Tony insists that it's possible. The senator demands that they send a man back in time after ten years of work. Either he'll write them a blank check or cut them off. Doug objects, saying that they can't risk a human life. Tony is willing to take the risk but Doug overrides him. The younger scientist angrily walks off and Doug and Kirk continue with their tour.
That night, Ton sneaks into the control room and activates the controls. He sees people moving in the upper gallery and runs into the Tunnel, disappear in a flash of light. Doug signals a red alert and everyone runs to their stations. Project scientist Ann MacGregor explains to Clark that Tony is in a radiation freeze, the first step in temporal relocation. They have no choice but to begin the countdown and complete the relocation. Once it has succeeded the scientists, including Ray Swain, try to get a lock on Tony's position. When Clark asks for more explanation, Doug snaps at him and the senator apologizes. Doug explains that after the radiation bath, they can establish a magnetic fix on Tony and locate him in time. If it doesn't work, then Tony will be lost in time forever.
Tony drifts through an endless void and finally touches down on the deck of an ocean liner. Althea Hall, sitting nearby, hears the noise but doesn't see how Tony arrived. She offers to call for help and Tony assures her that he's fine. When he comments about the ship, Althea says that it's supposed to be the biggest ship ever built. She invites Tony to sit and they exchange introductions. Althea mentions Teddy Roosevelt and her taking a trip to New York, and notes that she hasn't seen him in the dining room. Tony claims that he's been working in his room and taking meals there, and Althea mentions that it's Saturday, April 13. As he walks off, Tony tries to work out why the date sounds familiar... and then he sees a live preserver with the name of the ship on it: Titanic.
At Project Tic-Toc, Swain confirms that the power usage suggests that Tony couldn't have traveled more than a hundred years forward or back. When they find him, the monitors in the Tunnel will let them view him but the transmission is one-way. They hear bells, unaware that it's a steward signing the dinner notice. Meanwhile, Tony approaches Captain Smith and tries to warn him that the Titanic will sink after it strikes an iceberg. Smith believes that Tony is playing a practical joke and the scientist admits that he sounds insane. When Tony says that he was born in 1938 and is a time traveler, Smith has his officer Grainger confine Tony incommunicado as a confessed stowaway. Once he's taken away, Smith suggests to Grainger that Tony may be a saboteur for another shipping line. However, Smith tells Grainger to confirm iceberg movements just in case.
The team gets a lock on Tony and see the Titanic from a distance. Kirk recognizes it and tells the others that it is the Titanic. Ann has a team bring up historical files on the ship and the date that it went down, while Doug explains that Tony can die in the past just as readily as he can in the present.
Althea comes to see Tony after checking with Smith. She questions his motives and he tries to explain the concept of time. All he does is frighten Althea and she offers to go to Smith and tell him that Tony is harmless. He refuses to promise to stay out of the way and Althea. Outside in the hallway, she staggers and then takes some pills.
At Project Tic-Toc, the team spots Tony and locks in the coordinates. The guard threatens to put Tony in chains if he doesn't quiet down. Once he's alone, Tony calls to his teammates and tells them where he is and when. Doug confirms that his colleague is locked up in a cabin breached by the iceberg, and that the Titanic will sink in 14 hours. Kirk suggests that they pull Tony out. However, the process will suspend all of his bodily functions unless they transfer him to another time zone within seconds.
Doug has another idea: he'll go through the Tunnel in period clothing, free Tony, and make sure the two of them are among the 300 male survivors. He tells a research team to get him a 1912 newspaper, while Kirk vehemently disagrees. Doug appreciates Kirk's efforts to protect him but insists that he should try to prove his friend's experiment since he failed. Kirk reluctantly agrees and organizes a countdown while Doug prepares for the transition.
Once Doug dons period clothing, Clark gives him the 1912 newspaper and wishes him luck. Swain has overlaid his transit coordinates over Tony's so that he will arrive at the same time. Doug then enters the Tunnel and is sent through time. He arrives in the Titanic's boiler room and makes a hasty exit. Upstairs, Doug goes to a supply room to wash off the coal dust on his hands. A young French boy, Marcel, runs in with armfuls of food and hides behind the door. An officer comes in and asks if Doug has seen Marcel, an immigrant who is stealing food. Doug doesn't say anything and the officer goes on his way. Marcel thanks Doug for his help and the scientist asks if he has seen Tony. The boy knows where Tony is and takes Doug to the cabin.
When they get to the cabin, Marcel grabs a fire hose and unspools it, and then runs off. When the guard goes after him, Doug enters the cabin and explains how they homed in on him. Tony complains that now they're both stuck, but Doug shows him the newspaper he brought back. The young scientist figures that Smith will dismiss the newspaper as a hoax, and Doug suggests that they break into the radio room and send an SOS before the disaster. Tony agrees to the plan and lures the guard in, and Doug knocks the man out from behind.
The two scientists take the guard's gun and go to the radio room. They lock up the two operators and send an emergency signal. A Dutch liner picks up their CQD but Grainger and some sailors break in. After a brief struggle, they subdue Tony and Doug. Smith arrives and Doug shows him the newspaper. The captain casually takes it, has the sailors take them away, and throws the newspaper out a porthole. When the radio operator informs him that ships are responding to their distress signal, Smith sends out a signal telling them to disregard.
As midnight approaches, Smith goes to the main room and listens to Althea playing the piano. As he has a glass of wine, the Titanic shakes from a sudden impact and Smith goes to see Doug and Tony. He orders Grainger out and then asks how they knew about the iceberg. Doug repeats their explanation. Smith refuses to accept their explanation and insists that the Titanic is unsinkable. As they beg him to lower the lifeboats, another impact rocks the ship. Smith calls Grainger and tells him to prepare the lifeboats. Doug points out that the lifeboats will only hold a relatively small percentage of the ship's complement. Smith admits that he considers their presence a miracle, letting them save at least 750 lives. Tony suggests that they go on the decks to help some to survivor, and the captain agrees. As they go, Smith asks if they know what will happen to him, and Doug tells him that he will go down with his ship.
As the Titanic takes on water, the Tic-Toc scientists watch helplessly. They can remove them but Kirk realizes that Doug and Tony will be sent to some random point in time and space. Swain points out that it's a better fate than certain death on the Titanic, but Kirk isn't so sure.
Doug and Tony split up to get the passengers to the lifeboats. Tony finds Althea at the piano and she explains that there's no point in her taking up someone else's seat in a lifeboat because she has an incurable growth in her brain. She spent all of her money to buy a ticket to get to New York and meet with a doctor developing a type of operation known as "neurosurgery." Tony assures her that neurosurgery is a highly successful procedure and asks her to trust him and chooses life over death. After a moment she goes with him to the lifeboats.
Doug makes sure that Marcel and his mother get into a lifeboat. Elsewhere, Tony gets Althea to a lifeboat and she realizes she will never see him again. Doug finds Tony and tells him that there's trouble on another deck. As they get there, an explosion knocks them over the side... and the Tic-Toc scientists freeze them. They accelerate power before it's too late and send their friends back through the endless reaches of time. The Tunnel goes blank and the scientists admit that they have no idea where Doug and Tony might be.
Later, Jiggs returns Clark's briefcase as the senator prepares to leave. He promises that he'll maintain funding until they either recover Tony and Doug or there's no chance of their safe return. Swain assures Clark that they are developing new procedures every day and that they will eventually come up with an answer. Once the senator leaves, Kirk admits that all their efforts will mean nothing if the two scientists can't survive.
Tony and Doug arrive in the cargo hold of a space rocket on a countdown. The only door is locked and the two men get down on the floor so they're not knocked about as the rocket lifts off into space.