The Bucks outscored the Raptors 32-17 and held an 18-6 advantage in rebounds during the fourth quarter. It was Milwaukee's first victory in the Eastern Conference finals since defeating the Philadelphia 76ers on June 1, 2001.
"Hopefully, it speaks to our depth," Bucks head coach Mike Budenholzer told reporters. "I think we got a lot of guys that are capable and contribute. I think it speaks a little bit to the character of the group. They just stick with it."
Giannis Antetokounmpo had 24 points, 14 rebounds and six assists. Brook Lopez had a playoff career-high 29 points on 12-of-21 shooting, including a 4-of-11 mark from 3-point territory.
Lopez scored 13 of his 29 points in the fourth quarter.
"Obviously, big game from Brook on both ends of the court," Budenholzer said. "We feel like we can get better. To get this win after pretty significant days without playing, I think, hopefully, we'll be better between now and Game 2."
Milwaukee's Khris Middleton notched 11 points, 11 rebounds and four assists. Nikola Mirotic added 13 points and six boards.
The Raptors, who led by as much as 13 points and held an 83-76 lead entering the fourth quarter, went cold from the floor in the final frame. Toronto shot 5-for-22, and guard Kyle Lowry was the only Raptors player to record a made field goal in the last period.
"Turnovers, missed shots, we just didn't execute," Lowry told reporters. "We just didn't finish the game well."
Lowry had 30 points, eight rebounds and two assists. He shot 10-of-15 from the field and knocked down a playoff career-high seven 3-pointers.
Kawhi Leonard had a game-high 31 points with nine rebounds and two assists. Pascal Siakam added 15 points and six boards.
Game 2 is Friday night at Fiserv Forum in Milwaukee.