In the year 2058, Earth will soon be uninhabitable after the irreversible effects of pollution. The United Global Space Force serves as the planetary government. Professor John Robinson, lead scientist of the Jupiter Mission, will lead his family to the habitable planet Alpha Prime to prepare it for colonization by building a hypergate in orbit. The Jupiter 2 is equipped with a hyperdrive that allows faster-than-light travel, which will eventually be employed to evacuate the citizens of Earth. However hypergates must be constructed on Earth and Alpha Prime to provide stable points of departure and arrival. The project is accelerated after Global Sedition terrorist forces send two armed fighters to destroy the hypergate under construction. Major Don West, a fighter pilot from the hypergate defense force, manages to destroy the enemy fighters and is unwillingly drafted as the new pilot of the Jupiter Mission, as the previous pilot has been assassinated.

Dr. Zachary Smith is bribed by the Global Sedition to sabotage the mission and is betrayed by his employers, left as an unwilling stowaway as the ship blasts off. The sabotage causes the ship to veer towards the sun. Realizing that it would be impossible to escape the sun's pull at such close range, Major West and Professor Robinson decide to fly through the sun, using the ship's hyperdrive. Unfortunately, without a hypergate to warp to, the ship and its crew end up in a random (and apparently uncharted) part of the galaxy. Upon arrival, they encounter a "hole in space" in the vicinity of an extraterrestrial planet; the hole is presumably a gateway into the future. Major West takes the Jupiter 2 into the hole, where the crew encounter and board the Proteus, an Earth ship from the future which has been infested with carnivorous and cannibalistic silicon-based spider-like lifeforms. In the midst of the battle to escape the ship unharmed, Dr. Smith receives a deep wound from a spider's claw, and the Jupiter 2's robot is destroyed. Major West self-destructs the Proteus, destroying the spiders. However, the shock wave from the explosion damages the Jupiter 2, and they crash-land on the nearby planet.

On the mysterious planet, they locate a fuel source with which to refuel the damaged engines of the Jupiter 2. However, it lies in the center of a massive "bubble" of mysterious origin. Professor Robinson and Major West explore the bubble and discover it is actually an area of time distortion where alternate future versions of Dr. Smith and Will have constructed a time machine, powered by their Jupiter 2's power core, and are planning on returning to Earth at an earlier time to prevent the family from getting lost in the first place. They are all betrayed by the future Smith, who is revealed to have transformed into a gigantic space spider/human hybrid as a result of the spider scratch he received on the Proteus. He then reveals his plan to go back in time to Earth and spread his spider race across the Earth. Robinson soon battles Spider Smith, while Major West returns to the other Jupiter 2, without the power source, to try to evacuate the other Robinsons. John successfully stops Spider Smith by slashing him across the face with a dagger and sticking it into the eggsac on his back, causing the baby spiders to come out and start eating Spider Smith (Will had discoverd that the spiders eat their wounded while they were on the Proteus). Spider Smith dies when Robinson kicks him into the time machine's field while it is too small for his massive form, killing him.

The family attempts to escape, but the time bubble has made the planet unstable, and it is violently breaking apart. As a result of not retrieving the extra power core, the ship still does not have enough power to reach escape velocity. The stranded John Robinson watches as the Jupiter 2 is hit by debris and explodes in the sky. Future Will realizes his father does indeed love his family, and lets John use the time portal and travel back in time to the Jupiter 2 just before it launched from his planet. The power core could only fuel one trip back through time, and Future Will stays behind, wishing his family luck. Rather than attempt to escape into the atmosphere, John commands West to pilot the ship through the planet's core as it is breaking up, enabling them to use the planet's gravity to propel the ship through the other side. They escape, but the collapsed planet forms a gravity well that begins to suck in the Jupiter 2. Once again the Robinsons must activate the hyperdrive; however, this time they are able to target Alpha Prime using data downloaded from the Proteus' more detailed star charts. The film ends with the Robinsons and West activating the hyperdrive, presumably transporting the ship to Alpha Prime. The last lines in the movie are West's "Targeting Alpha Prime, I hope" followed by Will's reply: "Cool!".