Brandon Knight took over from there, leading the Bucks to their longest winning streak in almost three years.
Mayo drained a game-tying 3-pointer in the final second of regulation and Knight scored 12 of his 24 points in overtime as the Bucks beat the Los Angeles Lakers 113-105 on Wednesday night.
Antetokounmpo had a career-high 25 points in the win, including four during a 13-0 run in the third quarter that helped pull the Bucks out of a big hole.
Later, they trailed by six with just 36 seconds left after Jeremy Lin hit a 3 for the Lakers.
Milwaukee had three 3-pointers in the final minute of the game, with Knight's cutting the deficit to 94-91 with 31 seconds left.
After Lin missed a 3 at the other end, Mayo buried his tying 3 from the left corner with Wayne Ellington and Carlos Boozer in his face. The Lakers had just 0.5 seconds remaining and fumbled the inbounds pass as the buzzer sounded.
Knight started overtime with a 3-pointer and the Bucks never trailed after that in their fifth consecutive win.
It's the team's longest winning streak since a six-game run March 9-20, 2012.
Mayo and Khris Middleton had 21 points each for Milwaukee and Knight scored 22 of his 24 after halftime.
Boozer led Los Angeles with 28 points. Ed Davis had 20 rebounds in the loss and Ellington scored 19 on 5-of-12 shooting from 3-point range.
The Lakers have dropped 11 of their last 12 games.
The Bucks shot 50 percent from the field overall and 11-of-26 on 3-pointers ... Milwaukee has won four straight in the series and six of the last seven meetings ... The teams will meet again in Los Angeles on Feb. 27 ... The Lakers continue their road trip Friday in Orlando ... The Bucks play in Houston on Friday.