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 star has been incredible for his team this season, throwing himself in contention for the MVP award at some points, and he will be a major threat towards Boston not advancing to the second round of the playoffs if he is able to get a groove going on the court.
When Irving went down for the final time the Celtics' standing seemed in question, but the team responded with a six-game winning streak to solidify the 2-seed before coasting to the end with a 2-4 closing stretch.
Rozier finished with 21 points, three rebounds and four assists for the Celtics.
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Giannis Antetokounmpo showed out for the Bucks with 35 points, 13 rebounds and seven assists, with Middleton finishing with 31 points.
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.
Malcolm Brogdon: He was Milwaukee's most effective scorer off the bench on Sunday. The third-year guard made both free throws and put Boston ahead 110-106 with 18.8 remaining. But like most of the Bucks, Parker struggled to ever get into any kind of rhythm as he scored just two points while missing four of his five shot attempts.