The Bucks' scoring was led by the MVP candidate, who also grabbed 10 rebounds, and not far behind was Khris Middleton, who scored 28 points with seven rebounds.
Eric Bledsoe produced a solid performance, improving on his six points in the Bucks' loss in game one on Sunday to finish with 21 points and five rebounds.
The third quarter proved the turning point as the Bucks outscored the Celtics 39-18, with Antetokounmpo putting up 15 points alone in the penultimate quarter.
Kevin Durant led the way for the Warriors with 29 points and Klay Thompson added 21 points in the 115-109 victory at the Oracle Arena.
Durant was matched on points by James Harden, who suffered an eye injury in the first period but returned to the game, but it was not enough to hold off the Warriors, who now travel to Houston for game three.