Toronto were able to erase a double-digit deficit behind a 35-point game from Kawhi Leonard as they moved to within a win of reaching the NBA Finals for the first time in franchise history.
"We made shots and got stops on the defensive end," Leonard told TNT after the game.
"We wanted to come out here and get the win, we weathered the storm early."
Leonard came out at the start of the fourth quarter and helped inch the Raptors ahead.
He knocked down a pair of step-back three-pointers during the team's 10-0 run midway through the period.
The Bucks managed to stay in the game behind back-to-back three-pointers from Giannis Antetokounmpo and Brook Lopez, but could not do enough to keep up with the surging Raptors.
Milwaukee were up by as many as 12 points until Toronto got some help from Fred VanVleet, who finished with 21 points off the bench.
He shot seven of 13 from the field and seven of nine from three-point range and was plus-28 on the court.
Antetokounmpo finished with a team-high 24 points on nine-of-18 shooting from the field and two of three from long distance.
Eric Bledsoe chipped in 20 points and Malcolm Brogdon had 18 in the team's losing effort.
The Bucks will go back to Toronto for Game 6 on Saturday.