The game's story takes place immediately after the events of Crash Bandicoot 2: Cortex Strikes Back, in which Doctor Neo Cortex's space station is destroyed by Doctor Nitrus Brio's laser beam device. Pieces of Cortex's space station hurtle towards Earth and crash into a tropical mountain. This sets free an evil entity known as Uka Uka, the mastermind behind Doctor Cortex's previous schemes. Uka Uka confronts Doctor Cortex and calls him out for failing to retrieve the Crystals and Gems, both of which are a great source of world energy. However, since Cortex's bumbling also managed to set Uka Uka free from his prison, Uka Uka felt a very great sense of gratitude and generosity toward Cortex. Uka Uka then recruits Doctor Nefarious Tropy to join them in their latest plan. Tropy has created the Time-Twisting Machine, a time machine that allows the villains to travel through time to find the Gems and Crystals at their original points in the timeline.

At the home of the Bandicoots, Aku Aku senses Uka Uka's emergence and orders Crash and Coco inside. Aku Aku tells the two that Uka Uka is his evil twin brother and that he was locked in an underground prison centuries ago by Aku Aku to protect the world from his malice. Crash, Coco and Aku Aku go to the Time-Twisting Machine, where Aku Aku gives Crash and Coco the task of recovering the Crystals before Uka Uka and Doctor Cortex do so. Crash and Coco proceed to travel through time and collect the Crystals and Gems, thwarting Cortex's minions (including Tiny Tiger, Dingodile and Doctor N. Gin) along the way. Doctor Nefarious Tropy is also defeated, throwing the Time-Twisting Machine into disarray. Having obtained all of the Crystals and Gems throughout time, Crash eventually faces off against Cortex in the Time-Twisting machine's core while Uka Uka and Aku Aku fend each other off. Following Cortex's defeat, the Time-Twisting Machine implodes on itself, the heroes manage to escape from the calamity whereas Cortex and Tropy are transformed into infants and along with Uka Uka are left to remain in a prison of time.