The Rescue Rangers travel to the Space Centre to watch the launch of the new Spaceplane. However, on the way, Gadget accidentally flies the Ranger Plane through a wind sock and they end up falling through an open window.
Finding themselves in the astronauts' training area (and with nearly an hour to go until the launch) Chip and Dale begin a crash course in space training. Presently, with both chipmunks having "crashed" the flight simulator, it is time for the launch so the Rangers head to the control tower. On the way, Dale finds a spacesuit and decides to have a look inside.
Dale falls into the spacesuit and Chip climbs inside after his friend, intending to rescue him. Just then, however, two humans appear on the scene and take the spacesuit to the Spaceplane. Monty, Gadget and Zipper hurry to the control tower but are unable to stop the launch. Gadget, who had been looking forward to the launch, now feels terrible and blames herself for landing Chip and Dale in this mess.
Meanwhile, the Spaceplane has left Earth's atmosphere and Chip and Dale have escaped from the spacesuit. Dale is fooling around in zero gravity when he collides with Chip and the chipmunks accidentally knock a spacesuit free from its moorings. Just then, a female astronaut, Joy Rider, deploys a satellite and the loose spacesuit falls through the airlock, taking Chip and Dale (who have ended up inside the suit) with it.
Back on Earth, the other Rangers learn what has happened. Since the astronauts won't be retrieving the spacesuit until the end of their mission (which is scheduled to last two weeks) Gadget decides the Rangers will have to retrieve it themselves. At a junkyard, she builds a spacecraft (propelled by sticks of dynamite) which she, Monty and Zipper use to travel into outer space.
A length of rope with a loop on the end catches the spacesuit and Gadget prepares for re-entry. But Monty has jettisoned the parachute and raft she planned to use for the splashdown, believing it to be "junk". This means the Rangers now have no choice but to stow away on the Spaceplane.
Gadget, wearing a spacesuit consisting of a rubber glove (the fingers cover her limbs and tail) with some clear plastic for a helmet, leaves the spacecraft. She then uses a screwdriver to get the Spaceplane's doors open, while, back on the spacecraft, Monty fires the retro-rockets and propels the craft into the Spaceplane. There, the Rangers stow away in the food locker.
However, shortly after they arrive, the Spaceplane is struck by a meteor. The astronauts, who had been having a rest period, are woken by the jolt, but the resulting oxygen leak causes them to pass out. And, to further complicate matters, Mission Control loses remote flight control. The Rangers, arriving at the command deck to hear the astronauts being told to land before their oxygen runs dry, try to wake them but are unable to do so.
Next, Dale tries to contact Mission Control, but the humans are unable to understand animal speech. Gadget quickly realises the Rangers will have to land the Spaceplane themselves and turns to Chip and Dale, saying that it's a good thing they've had astronaut training. The chipmunks exchange uneasy glances, but Chip is determined to give this his best shot and sets to work.
Soon, the Spaceplane has re-entered the atmosphere as Chip and Dale work together to bring it down safely. But, then, the Rangers realise they are out of control and plunging dangerously close to the control tower - what's more, none of them knows what to do in such a situation. Luckily, Gadget draws on her knowledge of the Ranger Plane's controls and suggests they "pull back on the stick".
The Rangers follow her lead, with Chip and Dale operating one stick while Monty and Gadget deal with the other. As the Spaceplane touches down, one of its tyres bursts. The Rangers then hurry to hit the brakes but soon realise they aren't stopping.
The Spaceplane collides with some rocks, sending the Rangers flying. Woken by the jolt, the astronauts find that the Spaceplane has landed, even though none of them can remember doing it; they decide that the training they have had made the procedure for landing "seem easy". Later, when they attend their ticker tape parade, their car has five extra passengers.