Hill scored to begin the second overtime, giving Milwaukee its first lead since the opening basket of the game.
Gasol answered with a 3-pointer and Leonard finished a fast break with a left-handed dunk, putting Toronto ahead, 108-105, with 3:13 left.
Khris Middleton of the Bucks shot 3 for 16 from the field, but one of his baskets tied the score with 2.2 seconds to go in regulation. He finished with 9 points.
After suggesting on Saturday that he might change his lineup, Raptors Coach Nick Nurse stuck with his usual starters but gave Powell 30 minutes, the most he has played in a game this postseason.
Toronto fell behind, 9-0, early in a blowout loss in Game 2, but turned that around in Game 3. After Antetokounmpo made a layup for the opening basket, Siakam replied with a hook shot, Gasol followed with a 3-pointer, and the Raptors did not trail again in regulation.
Powell scored 10 points on five shots in the first quarter, including a pair of 3-pointers, and Toronto finished the period leading, 30-21. Gasol, who had 8 points in Games 1 and 2 combined, also made a 2-pointer from long range and scored 8 in the quarter.
The Bucks shot 7 for 21 in the opening quarter. Five of their baskets were 3-pointers.
Leonard scored 11 points in the second and Lowry added 8, but Pat Connaughton made two of Milwaukee’s five 3-pointers as the Bucks closed the gap. The Raptors led, 58-51, at halftime.
Siakam scored 8 points in the third quarter, but the Raptors had six turnovers, leading to 9 points for the Bucks. Toronto took a 77-75 lead into the fourth.