The game could have implications later in the season since both the Bucks and Cavaliers are likely to battle for lower playoff positions in the Eastern Conference.
Gooden's foul shots gave the Bucks a four-point lead and allowed them to survive a 3-pointer by Cleveland's Alonzo Gee at the buzzer.
The Cavaliers missed a chance to win the game in regulation when Antawn Jamison failed on both free throw attempts with 4 seconds left in the fourth quarter.
Brandon Jennings led the Bucks with 24 points and eight assists. Gooden had six of his 19 points during overtime.
Jamison delivered a season-high 34 points. Cleveland rookie Kyrie Irving missed his second straight game with a concussion.