Kawhi Leonard had 27 points and 17 rebounds to lead the Toronto Raptors into the NBA finals for the first time with a 100-94 victory over the Milwaukee Bucks on Saturday night.

The Raptors overcame a 15-point deficit to win the series in six games and will host the Golden State Warriors in Game 1 of the NBA finals on Thursday night.

Pascal Siakam scored 18 points, Kyle Lowry had 17 and Fred VanVleet 14 for the Raptors, who used a 26-3 run late in the third quarter and early in the fourth to turn the game in their favor.

Giannis Antetokounmpo led the Bucks with 21 points and 11 rebounds, but the NBA’s top team in the regular season saw its bid for a first finals berth in 45 years come to a disappointing end with a fourth consecutive defeat.

Down 76-71 to start the fourth, the Raptors tied it with an 8-2 run while Leonard and Antetokounmpo were both on the bench. Ibaka’s dunk with 10:32 to go tied it at 78.

Antetokounmpo returned after a timeout, but Leonard kept sitting. That didn’t matter to Toronto, with Siakam’s basket giving the Raptors an 80-78 lead, their first lead since it was 6-3.

Leonard’s one-handed slam after Lowry’s steal gave Toronto an 87-79 lead with 6:46 to go before the Bucks responded. George Hill answered with a layup, Brook Lopez converted a three-point play and Antetokounmpo scored to cut it to 87-86 with 5:19 to go.

Drake sports a sweatshirt in support of Kawhi Leonard during Game 6. Photograph: Nathan Denette/AP

Lowry and Lopez swapped baskets before Gasol’s three put the Raptors up 92-88 with 3:50 left. After another basket by Lopez, Leonard made a three to push Toronto’s lead to 95-90 with 3:04 to play. It was Leonard’s first three after missing his first seven attempts of the game.

Toronto made 12 of 27 three-point attempts, including four of eight in the fourth quarter.

Siakam, who missed a pair of free throws late in the fourth quarter of Toronto’s double-overtime win in Game 3, hit one to make it 98-94. Leonard grabbed the rebound on the second and was fouled. He made both, putting the Raptors up 100-94 with 3.9 seconds to go.

Brogdon and Middleton each made a pair from long range as the Bucks shot 6 for 9 from three-point range in the first and closed the quarter with 10 unanswered points to lead 31-18. Toronto shot 6 for 19 in the opening quarter, missing six straight twice in the first 12 minutes.

The Bucks extended their lead to 38-23 on a three by Ersan Ilyasova with 7:46 left until half. Toronto cut the gap to 46-43 on a three by VanVleet with 1:07 left in the second, but Eric Bledsoe answered with a three and Antetokounmpo split a pair at the line, giving the Bucks a 50-43 advantage at the intermission.

The lead went back to 15 in the third before Leonard finished the period with a flourish. He had eight points in the final 2:01 and Toronto closed with a 10-0 run, cutting a 15-point deficit to 76-71.