MILWAUKEE — The Toronto Raptors are in uncharted territory. One win from the NBA Finals.

Kawhi Leonard scored 35 points and added nine assists and seven rebounds to lead the Toronto Raptors to a thrilling 105-99 victory over Milwaukee on Thursday in the most important game in franchise history.

The Raptors can book their ticket to the finals with a win Saturday in Toronto.

It was Leonard's 11th 30-plus performance for the Raptors, who took a 3-2 lead in the best-of-seven Eastern Conference finals with their historic win. Never before has Toronto won three games in a conference final.

Three days after his girlfriend gave birth to their son, Fred VanVleet had seven three-pointers as part of a playoff career-high 21 points. Kyle Lowry, playing through what he called "pretty bad" pain with a sprained thumb, had 17 points, seven rebounds, and six assists. Pascal Siakam had 14 points and a game-high 13 rebounds.

Giannis Antetokounmpo had 24 points to lead Bucks, who with 60 wins (two more than Toronto) had the best record in the league in the regular season. The Bucks hadn't lost three straight games all season.

The Raptors stumbled out at the start, digging themselves an early 14-point hole with horrible shooting. But, thanks to their stifling defence, they clawed their way back to take their first lead late in the second quarter. The Bucks led 75-72 with one quarter to play.

VanVleet connected on his sixth three of the night, then Leonard drained two in a row and the Raptors took a four-point lead with 7:56 to play. A Siakam dunk capped a 10-0 Raptors run to give them an eight-point cushion. The Bucks rallied to cut it to four with 5:31 to play.

Marc Gasol connected on a three, his first points of the game, to put Toronto up by seven, but Antetokounmpo's three made it a two-point game with four minutes left. Brook Lopez and VanVleet traded threes, then Leonard drained three free throws to give the Raptors a four-point lead with a minute to play.

Gasol made one of two free throws with 34.7 left. The Raptors got the ball back on the next possession when a video review showed the ball bouncing off Milwaukee's Malcolm Brogdon and out of bounds.

The Raptors inbounded the ball to Leonard, who heaved the ball over a Milwaukee swarm to Lowry, who passed the ball to a wide-open Siakam. The forward sauntered in for a seemingly easy dunk with 16 seconds to play and it was game over.

Leonard's health — he missed all but nine games last season with San Antonio — was worrisome after he'd been noticeably hobbling in Game 4, two nights after a double-overtime win. But Raptors coach Nick Nurse was confident in his star.

"I expect him to be good," Nurse said pre-game. "I think he's a little fresher today maybe than he was a couple days ago, it seems, in just his demeanour and his moving around in general. I gave him the option to skip shootaround today, and he said, 'No, I'm going.' He wanted to come."

This is only the second appearance in the conference final for the Raptors, who stole two wins off LeBron James and the Cleveland Cavaliers in an otherwise lopsided series before being ousted in six games in 2016.

The Raptors' horrible start Thursday was reminiscent of the Bucks' 125-103 Game 2 rout in Milwaukee. Toronto made just four of 12 three-point attempts, and when Antetokounmpo threw down an alley-oop dunk from Eric Bledsoe it put the Bucks up by 12 points before the game was four minutes old. A jumper from Bledsoe stretched Milwaukee's advantage to 14.

But the Raptors pulled to within six points on a VanVleet three. They trailed 32-22 heading into the second quarter.

The Raptors held Milwaukee to 1-for-12 shooting to start the second, and Lowry's three-pointer with 5:09 left in the quarter capped a 14-2 Raptors run and gave Toronto its first lead. Antetokounmpo missed on a dunk on the Bucks' next possession, then a pullup jumper from Leonard put Toronto up by four.

The Bucks took a 49-46 lead into the dressing room at halftime.

Milwaukee opened the third with a 14-4 run, but VanVleet — with three threes in the quarter — kept the game close and the Raptors trailed by just three with a quarter left to play.

Back in Toronto, thousands of fans packed Maple Leaf Square outside Scotiabank Arena to watch the game on the building's giant screen. Drake took the stage and had the crowd roaring. The Canadian rapper, and the Raptors' "global ambassador," has been a lightning rod after his antics in Game 4 — he was on the court cheering and heckling and squeezed Nurse's shoulders. Bucks coach Mike Budenholzer was among the people who weren't impressed.

The Fiserv Forum crowd included rapper Gucci Mane, and Green Bay Packers quarterback Aaron Rodgers and offensive tackle David Bakhtiari who guzzled beer on the Jumbotron, Bakhtiari downing three to Rodgers' one.

A Game 7, if needed, would be back in Milwaukee.

The Golden State Warriors, who completed a sweep of Portland on Monday, await the winner.

Note to readers: This is a corrected story. A previous version had the incorrect series score in the long headline