In the mid-1960s, a small-town Pennsylvania band named "The Oneders" (later changed to "The Wonders") stumbles upon success after their original drummer breaks his arm. Guy Patterson, a jazz enthusiast working at his family's appliance store, is recruited as the replacement. Guy injects a new, upbeat tempo into the band's slow ballad, transforming "That Thing You Do!" into a hit single. Their energetic performance style quickly catches fire, and before long, they are signed to a recording contract by Mr. White, a fast-talking manager from Play-Tone Records.

As their popularity grows, the band experiences the highs and lows of newfound fame. They embark on a national tour, make television appearances, and grapple with the pressures of the music industry. However, the rapid rise to stardom also tests their personal relationships and the cohesiveness of the band. Guy's blossoming romance with Faye, the girlfriend of the band's frontman, and internal struggles among the band members start to threaten their success. The story captures a poignant moment in the band's history, highlighting the excitement and challenges of their fleeting brush with fame.