HOUSTON -- The Houston Rockets were down by one point with no timeouts and mere seconds remaining Thursday night.

In that moment James Harden was the only one they wanted to have the ball. And as usual their star delivered.

Harden scored 35 points, including the game-winner with 2.7 seconds left, and the 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.

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.@JHarden13 πŸ”₯ https://t.co/NXQuZJzk5x

β€” NBA on TNT (@NBAonTNT) April 22, 2016

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.

"The last shot was typical of what James does," coach J.B. Bickerstaff said. "The move, we've seen before. The finish, we've seen before. You do get spoiled by it at times, but in these biggest of moments, you can't help but appreciate 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.

Draymond: I cost us this game. I was horrible"

β€” Ethan Strauss (@SherwoodStrauss) April 22, 2016

draymond right now pic.twitter.com/3f8e3i7b8y

β€” MiGuel (@SKF_Axis) April 22, 2016

Why would the Warriors ever ever ever inbound the ball to Draymond green with 2.6 seconds left 5ft behind the 3point to win the game ???

β€” Checks & Balances (@RealLilLeeks) April 22, 2016

Kerr's face when Draymond lost the ball pic.twitter.com/OxWXBXaami

β€” Ξ²LΞ”ST MΞ”STΞ£R (@djhomicide) April 22, 2016

When Draymond rolled to ball off his foot https://t.co/mLwRT9VeFv pic.twitter.com/2T72xkYWVj

β€” Jamie Faue (@BrickWallJamieF) April 22, 2016

Warriors lost without their starting PG. Now they know how the teams they beat in the playoffs last year felt.

β€” Not Bill Walton (@NotBillWalton) April 22, 2016

Damn Draymond! πŸ˜‚#Donkey pic.twitter.com/lQsYH3FHy6

β€” C E D R I C K (@C_David02) April 22, 2016

When they threw the ball to Draymond pic.twitter.com/YOZNTR9wXY

β€” puch1 (@Puchwop) April 22, 2016

Draymond Green right now be like... #Warriors #GoldenState #Oakland #GSW #Houston #Rockets #Playoffs #Clippers #Tog… pic.twitter.com/QBxwoWvLTQ

β€” Clippers Selfie (@clippersselfi1) April 22, 2016

"I cost us the game," Green said. "The world will think I'm talking about that last turnover but I'm not. That happens. I was awful the whole game. I care about that turnover, but I cost us the game way before then."

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 wasn't on the bench for this one and didn't officially speak to reporters after the game, but did say that he wasn't on the bench because he expected to play and didn't bring a suit to Houston.

After a plea from 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.

"We were on attack," Harden said. "We were just the aggressor from the beginning of the game and we kind of rode that wave out."

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

"It was what we planned and what we talked about," Bickerstaff said. "They made their run, but we didn't fold, we didn't cave in."

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.

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

Kerr refused to use Curry's injury as an excuse.

"Whether Steph's here or not, we should perform at a high level, which we did for much of the game, but we've got to eliminate some of the mistakes," he said.

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.

HELPING OUT

Rockets owner Leslie Alexander donated $500,000 on Thursday to Houston Mayor Sylvester Turner's Greater Houston Storm Relief Fund to aid those affected by flooding in the city this week.

"The donation from Leslie Alexander and the Houston Rockets speaks volumes about their commitment to this city," Turner said. "They recognize the need of so many Houstonians and are using a significant portion of their dollars to assist."

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. ... Howard got a technical in the first half.