The scene changes to a flashback, in which a small dinosaur is being chased by a hungry T. rex in what is presumably the Late Cretaceous Period. He is interrupted when a gigantic futuristic craft knocks him down. A small green alien (later identified as Vorb) flies out of the craft and starts advertising "Brain Grain Cereal", which increases the intelligence of whoever (or whatever) eats it. After the T. rex tries to eat him, Vorb lures the dinosaur into the craft, where he force-feeds him 210 portions of Brain Grain. The T. rex transforms, becoming intelligent, able to speak, and more gentle-looking. The T. rex receives the name Rex, and is introduced to other dinosaurs who have been fed Brain Grain Cereal: Dweeb (a Parasaurolophus), Woog (a Triceratops), and Elsa (a female Pteranodon). Rex is surprised to discover he can read, while the rest of them seem more at ease with their newfound intelligence.
After a hot dog lunch, the dinosaurs meet Captain Neweyes, operator of the winged time ship and inventor of Brain Grain. He demonstrates his Wish Radio, which picks up people's wishes (usually children's, as they wish the hardest). The captain also reveals that in the early nineties many wishes revolve around seeing "real dinosaurs", and explains that he gave the dinosaurs Brain Grain so they could decide for themselves whether or not to go visit the children of the future.
Rex and his friends accept, and Captain Neweyes informs them that there are two people to keep an eye out for: Dr. Bleeb, a scientist from the Museum of Natural History, and Professor Screweyes, Captain Neweyes's insane brother. He instructs them to find Dr. Bleeb, who is expecting them, and to avoid Professor Screweyes and his Eccentric Circus. The timeship travels to New York City, circa 1993. Vorb supplies the flightless dinosaurs with parachutes and Elsa with a raft.
They drop into one of the city's rivers, accidentally capsizing a boy and his lashed-together raft. After fishing him out of the water, he introduces himself as Louie. When the raft approaches the shore, they all lean back in appreciation of the skyline, and Rex unbalances, falling off the raft. Rex can't swim, so Louie jumps into a nearby backhoe and lifts him out of the water. Just after Louie and the dinosaurs leave the scene, Dr. Bleeb enters with posters advertising a new dinosaur attraction at the museum (Dr. Bleeb's unfortunate timing is a repeating gag in the movie).
Louie hides his new friends in a back alley, explaining people will panic if they see them. He focuses on Elsa, calling her a bat and asking if she can fly. In retaliation, she picks him up and carries him into the air. While in flight, Louie notices a crying girl on the balcony of a building and has Elsa return to her. They speak with the girl and learn she is upset because her parents won't be home for Thanksgiving. She agrees to join them and Elsa flies them both back to the alley. She introduces herself as Cecilia Nuthatch.
The dinosaurs have explained they need to get to the museum, and Louie has the idea of disguising them as floats in the Macy's Thanksgiving Day Parade. All is going well until Rex decides he can't deny the children's wishes of meeting a real dinosaur and reveals himself after performing a song of his own and then shaking hands with a balloon of a Apatosaurus. The balloon deflates and falls on all of them. The dinosaurs are forced to flee from the police and National Guard and are separated from Louie and Cecilia. Rex then falls on the bed of a red Dodge Dakota, and uses it as a Skateboard. The dinosaurs (including the truck) are then chased into a condemned building, which is demolished while they are inside. The blast destroys the truck and sends them flying into Central Park. Meanwhile, Louie and Cecilia have made their way to Central Park as well, and Louie is entranced by a poster advertising Professor Screweyes's Eccentric Circus. They find their way to the circus proper, where they meet the Professor himself and are conned into joining, signing a magical blood contract.
A moment too late, the dinosaurs locate the children. At first, Professor Screweyes is frightened of them, but when he realizes they are intelligent he offers a trade: the children's freedom for themselves, to use in his act. The dinosaurs agree and are fed Brain Drain, the antidote to Brain Grain, and the dinosaurs are returned to their natural state and caged.
The kids wake up the next morning and are warmly greeted by Stubbs, a circus clown who wants to show off his hilarious act but is not allowed by the professor. At their demand, he reluctantly shows them what has become of their dinosaur friends: they are once again dangerous, vicious animals. Louie and Cecilia talk Stubbs into sneaking them into the show that night, where the dinosaurs will be featured.
That night, the three disguise themselves in monster costumes and watch as the dinosaurs are revealed and 'hypnotized' by the professor. As Screweyes forces Rex to do what he commands, a raven gets into the control room and accidentally repositions a spotlight, shining it in Rex's eyes. This breaks the professor's hold over him and he moves to attack the professor. Cecilia wishes for nothing bad to happen as Louie runs forward to try and reason with the beast. Eventually, Louie's impassioned pleas reach Rex, and he transforms back into his intelligent self. Louie and Cecilia hug the other dinosaurs, which returns them to their intelligent forms as well.
Just then, Vorb flies into the tent and directs gunners on the timeship to destroy the chains shackling the dinosaurs. Captain Neweyes descends into the ring via a hydraulic platform and tells Cecilia he'd heard her wish that "no bad happen". She and Louie then kiss. And then fireworks appear exploding out of the sky over the circus tent and Louie, Cecilia, the dinosaurs, and everyone else in the circus tent. Stubbs finally speaks his mind, hitting his boss with every gag he's got and quits amid the audience's laughter. The dinosaurs and children board the captain's platform as he asks his brother to forsake his twisted ways and join them. Professor Screweyes refuses, and Captain Neweyes returns the platform to the ship, which departs.
The professor is left alone in the dark, and his fear overcomes him. A flock of ravens surrounds him and perch on him, completely hiding him from sight, before scattering and revealing all that remains of Professor Screweyes: the screw that replaced his left eye. The last raven picks it up and flies off with it.
Captain Neweyes takes the dinosaurs to the Museum, where they finally meet Dr. Bleeb. She has arranged an exhibit where the dinosaurs pose as models while the parents are there, but after she ushers them out of the room, the dinosaurs come to life to meet the children, thereby allowing them to meet real dinosaurs.
The movie ends with Rex and Buster back on the golf course, though it is now sunset. Rex provides an epilogue, explaining that Louie and Cecilia are now a couple and that Cecilia reconnected with her parents. Buster picks up on the point and returns to his family. Rex walks off into the sunset, presumably to return to the Museum, where the other dinosaurs are waiting.
There was also an adaptation of the movie for the Game Boy.