Struggling boxing manager Moe is having lunch with three of his fighters who are threatening to quit in anger over not being paid. Upon hearing the song "Pop Goes the Weasel" being played by a violinist, the timid waiter attending to the group goes into a violent fugue state and knocks out all three fighters and the restaurant owner. Moe recruits Curly as a boxer and persuades Larry to play the tune at ringside so Curly can easily defeat his opponents and win prize money. Fighting under the name "K.O. Stradivarius," Curly quickly becomes the top contender for the heavyweight championship. As Curly trains on a rural road under Moe's supervision, they notice a young lady whose car is stuck in a ditch. Moe tries to help her, urging Curly not to get involved, but eventually asks Larry to play "Weasel" so Curly will have the strength to free the car. Curly rides away with the lady; on the night of the title bout, Moe finds them together in a dressing room and hits Curly, telling him to avoid women and go to the arena. Seconds into the first round, reigning champion Killer Kilduff knocks Curly out of the ring and onto Larry, breaking his violin. Larry frantically rushes through the streets in search of anything that will play "Weasel" as Kilduff mercilessly pummels Curly. He finds a radio broadcasting the tune and hurries back to the arena with it. The music revitalizes Curly, but it ends just as he is about to land a knockout punch and the fight turns in Kilduff's favor again. An infuriated Moe smashes the radio over Larry's head and sends him out to find something else they can use. Larry commandeers a politician's campaign truck that is playing the tune, drives back to the arena, and crashes in through a side wall. Curly revives again and easily knocks Kilduff out to win the championship, then accidentally knocks out Moe and Larry as the music keeps playing.
The script for Punch Drunks was written by the Stooges, credited as "Jerry Howard, Larry Fine, and Moe Howard". According to Moe, the initial treatment of the script was originated by Moe; on its strength, the studio decided to produce the Stooges' next film sooner than scheduled. Filming was completed May 2–5, 1934. In 2002, Punch Drunks was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant", the only Stooge film to achieve such an honor.