The Celtics were up 108-106 in overtime when Al Horford collected a rebound and got it ahead to Rozier, who was fouled.
Boston's Terry Rozier hit the expected game-winner for Boston to take a three-point lead with just over a second left.
The Bucks are implementing a "blackout" of the BMO Harris Bradley Center during their series with Boston, wearing black, using their black "Fear the Deer" court and encouraging fans to wear black, giving away black t-shirts for games three and four.
SRH celebrate their first ever IPL win at Eden Gardens against KKR
They brutally punished Boult as 15 runs came in his second over, with Yadav hitting two fours and Lewis striking his first six. Meanwhile, pace bowler Adam Milne has become the 10th Kiwi to pick up a contract this season.
Sure, keeping Antetokounmpo contained will give the Celtics a good chance of advancing to the second round of the playoffs, but the Bucks have other dangermen in Eric Bledsoe and Khris Middleton which Boston must consider.
The final minutes of regulation were all over the place, with both teams trading huge three-pointers, before Khris Middleton sent it into OT, with the biggest shot of the day.
Jaylen Brown: Strong play all game from Jaylen Brown as he finished with 20 points on 9-for-19 shooting to go with four rebounds, four assists and a blocked shot. Middleton poured in 31 points and added eight rebounds and six assists. He scored 21 points off the bench to go with seven rebounds which was also tops among reserves for both teams.
Check it out. The ball just got off his fingertips.