HOUSTON -- The frantic, final moments nearly undermined all the Houston Rockets built in scratching out a double-digit lead, but James Harden took advantage of the disarray by doing what he does best.

Harden nailed a step-back jumper with 2.7 seconds left, and the Houston Rockets claimed a 97-96 victory over the Golden State Warriors on Thursday night in Game 3 of a Western Conference first-round playoff series at Toyota Center.

The defending champion Warriors, playing a second consecutive game without All-Star guard Stephen Curry (right ankle sprain), still lead the best-of-seven series 2-1. Game 4 set for Sunday at Toyota Center.

The Rockets blew a 17-point lead and trailed with 10.6 seconds left after Trevor Ariza threw away an inbounds pass that facilitated a fastbreak layup by Warriors reserve guard Ian Clark.

With Houston out of timeouts, Harden followed with a quick dribble, darted into the lane and spun free before nailing a 10-foot jumper.

Warriors forward Draymond Green dribbled the ensuing inbounds pass off his foot and out of bounds for a turnover with one second left.

"A lot of people just get nervous and don't want to be in that situation," said Harden, who scored a game-high 35 points. "For me, I strive in moments like that, so you just have to have confidence."

Harden added eight rebounds and nine assists. Donatas Motiejunas produced 14 points and 13 rebounds, while Dwight Howard also recorded a double-double (13 points and 13 rebounds) plus two blocks.

Reserve forward Marreese Speights led Golden State with 22 points in 18 minutes. Klay Thompson contributed 17 points and eight rebounds, and Shaun Livingston, who again filled in for Curry, added 16 points.

What Speights started in the second quarter and carried through the third, Livingston picked up in the fourth. Following a pair of Harrison Barnes free throws that sliced the Warriors' deficit to six points, Livingston added three jumpers, the last with 8:59 left to cut it to 81-80.

Despite following that spurt with a three-minute drought, the Warriors hung tough. Trailing 88-80, they rallied with seven consecutive points and later took their first lead since 2-0 when Clark nailed a floater with 1:25 left.

That push to the lead seemed to cripple the Rockets, who instead found enough gumption to at minimum earn another trip to Oakland.

"Well, I'm not really encouraged. This is how we were supposed to play," Warriors coach Steve Kerr said. "We should have actually played better. We made too many mistakes."

Golden State surrendered 20 points off 14 turnovers and missed 19 of 25 3-point attempts.

The Rockets sought early energy, and already leading 21-15, closed the first period with a 10-3 run.

Harden was the linchpin, tallying seven consecutive points before Ariza turned a turnover into a transition dunk. Harden closed the quarter with a free throw, a pull-up jumper plus a basket following his offensive rebound for a 13-point advantage entering the second.

"They are who they are," Livingston said of the Rockets. "When you play a team like that, they can go on big runs. James got going a little bit, got to the free-throw line, but I think we just got to play better as a team."

Houston extended to a 53-36 lead when Jason Terry and Harden sank 3-pointers, but that was when Speights went on his scorching streak.

The Warriors closed the half with a 9-0 run following a technical foul on Howard. Speights drilled his third trey of the half with 2.4 seconds left to cap his 14-point period and cut the deficit to 55-48 at the break.

In the third, every time Houston seemed poised to pull away, Speights delivered. He posted all eight of his points in the period inside the last 4:09, including a dunk and layup that pulled the Warriors within 78-72.

Things went completely haywire in the fourth. Harden proved equipped to handle the tension and the madness down the stretch.

"When he gets to his sweet spots, can't nobody guard him. Nobody. Don't matter who it is," Ariza said of Harden. "He showed that again, time after time tonight."

NOTES: Warriors G Stephen Curry was inactive for a second consecutive game as Golden State took a cautious approach to his return from a right ankle sprain. While Curry's ankle is improving, the team opted against playing him following four days of inactivity. If Curry participates in three-on-three drills on Friday and five-on-five Saturday, chances are good that he will return for Game 4 on Sunday. Shaun Livingston again started in place for Curry. ... Rockets owner Leslie Alexander will donate $500,000 to the Greater Houston Storm Relief Fund established by Houston mayor Sylvester Turner. The check was presented during Game 3 on Thursday night. Heavy rains and floods ravaged the city this week. ... Rockets interim coach J.B. Bickerstaff stuck with his Game 2 starting lineup in part because F Donatas Motiejunas brings a skill level plus the decision-making that matches up well against the Warriors' defense.