Brogdon wound up with 12 points and 10 assists as Indiana won its fourth straight.
T.J. Warren made an obscene gesture after his ejection.
The Pacers recovered in the second period to trail only 64-60 at halftime. Young had 30 points at the break, his career high for first-half scoring.
Aaron Holiday scored 25 points.
Oladipo injured his right knee in January 2019 and was temporarily assigned to the team’s G League affiliate in Fort Wayne in November.
The Pacers are 0-2 against Milwaukee this season, losing 102-83 at home on Nov. 16.
Indiana snapped a seven-game losing streak in the series — including Boston’s first-round playoff sweep last season.
The Mascot Hall of Fame shared a live video of the announcement to its Facebook page.
T.J. Warren scored 25 points and Domantas Sabonis had 19 points and 15 rebounds for the Pacers.
The Pacers have won seven of their last eight games.