Grandmother Hatsu has a birthday. She wants it to be a special day, and is eagerly waiting for her presents. However, father Taneo, mother Etsuko, son Tsuyoshi and daughter Ririka have all forgotten about that. They have to buy last-minute presents for the grandmother, and make it home in time for the party. Sounds simple? Not quite: each member of this completely ordinary, working-class family is delayed by inexplicable obstacles, which involve, among others, bank robbers, UFOs, miniaturization, and a giant teddy bear who is out to demolish Tokyo.

Incredible Crisis is entirely composed out of 24 predominantly action-oriented mini-games. Most of them are unique, though a few are repeated throughout the course of the game. Among these mini-games are synchronized dancing, various driving sequences, simple obstacle-dodging, shooting, and others. A few mini-games deviate from the action style, e.g. a quiz or a puzzle that involves calculating an item's weight.

The mini-games must be first completed in a specific order, tied by an overarching story told by CG animated cutscenes. Afterwards, they can be accessed directly from the main menu.