HOUSTON - James Harden scored 35 points, including the game-winner with 2.7 seconds left, and the Houston Rockets took advantage of Stephen Curry's absence to get a 97-96 victory over the Golden State Warriors in Game 3 of their first-round playoff series on Thursday night.

The victory cuts Houston's deficit to 2-1 in the best-of-seven series. Game 4 is Sunday in Houston.

Shaun Livingston stole a pass from Trevor Ariza and Ian Clark's layup put Golden State up by one with 10.6 seconds left. Harden then took it to the other end and stepped back for the jump shot to win it.

Golden State had a chance to win it after that, but Draymond Green dribbled the inbounds pass off his foot and out of bounds.

Marreese Speights came off the bench to lead the Warriors with 22 points and Klay Thompson had 17.

The Warriors blew out Houston in the series opener with Curry on the court, and pulled away late in Game 2 to go up 2-0 despite last year's MVP watching from the bench with a sprained right ankle. Curry was not on the bench with the team for this one and it was unclear where he watched the game.

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After a plea from coach J.B. Bickerstaff that his team be "nastier," the Rockets were much more aggressive and scrappy than they had been in the first two games and led by as many as 17 points in the first half.

Dwight Howard added 13 points, 13 rebounds and had two blocks for Houston and Michael Beasley finished with 12 points.

Andre Iguodala made a 3-pointer to cut the lead to 93-92 with about 2:45 remaining and Clark gave Golden State its first lead since 2-0 on a jumper that made it 94-93.

Beasley gave Houston a 95-94 lead with two free throws with 41 seconds left.

Golden State, which set the NBA record for wins in a season with 73, had won 14 of 15 and six straight over Houston before Thursday night's loss.

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Golden State used an 8-1 run, led by six points from Livingston, to cut the lead to 81-80 with 9 minutes remaining. Harden scored the next five points to power a 7-0 run that pushed the lead to 88-80 midway through the quarter.

Curry was feeling better on Thursday and wanted to play, but the Warriors decided the chance of him re-injuring his ankle before it was fully healed wasn't worth the risk. Coach Steve Kerr said they will have a better feel for his availability for Sunday after they see how he responds to the next two days of practice

Houston led by 12 points in the third quarter before a 10-2 spurt by Golden State, with six points from Speights, cut the deficit to 78-72 entering the fourth quarter.

The Rockets led 31-18 at the end of the first quarter thanks to 14 points by Harden. Howard was active early, coming from several feet away to leap and block a shot by Festus Ezeli that caused him to crash to the court in the first quarter.

They were up by 16 with about 2 1/2 minutes left in the first half before Golden State scored the last nine points of the second quarter to cut the lead to 55-48.

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Things got a bit testy in that span after Howard picked up his third foul when he got tangled up with Andrew Bogut fighting for a rebound. Howard received a technical after throwing the ball into the stands in frustration after getting the foul.

TIP-INS

Warriors: James Michael McAdoo had one point and four rebounds in his 2016 playoff debut. He appeared in five games in the playoffs last season. ... Speights, who didn't attempt a 3-pointer in the first 29 playoff games of his career, was 3 of 6 on 3s on Thursday. ... It was the first road game Curry has missed since he also sat out in Houston in a win on New Year's Eve.

Rockets: It was Harden's 12th career playoff game with at least 30 points. ... Donatas Motiejunas had 14 points and 13 rebounds for his first career double-double in the postseason.