HOUSTON — The Houston Rockets are heading to the Western Conference finals for the first time in 18 years after overcoming a 3-1 series deficit to eliminate the Los Angeles Clippers.

“It’s the ultimate confidence-booster,” James Harden said. “There’s only a handful of teams that’s done that. We fought back. We fought three really hard games and came away with it.”

Harden scored 31 points, Dwight Howard had 16 points and 15 rebounds and the Rockets never trailed in a 113-100 victory over the Clippers on Sunday, sending them to the conference finals for the first time since 1997.

It’s the ninth time in NBA history that a team has overcome a 3-1 series deficit to win a playoff series.

The Rockets overcame a 19-point third-quarter deficit in Game 6 on Thursday night to stay alive. No such heroics were needed Sunday when they were up by 17 after three and Howard opened the fourth quarter with a 3-point play to push it to 88-68.

“When you’re down 19 on the road, it’s easy to give in and just say, ‘Maybe next year,”’ Harden said. “But I think the injuries throughout the entire year kind of made us fight through adversity no matter what. We always find a way to fight, and another case was being down 3-1.”

Blake Griffin scored five points in a 9-0 run to cut the lead to eight points with less than 2 1/2 minutes remaining. Harden made a pair of free throws after that, but a dunk by DeAndre Jordan got the Clippers within eight again. This time, Trevor Ariza hit a 3 from the corner to secure the victory.

Howard was nervous until Ariza hit the final 3 and worried the Clippers might be the ones to orchestrate an unlikely comeback this time.

“Please, we can’t let them pull an us on us,” Howard said he was thinking during their late run.

Griffin had 27 points and Chris Paul had 26 points and 10 assists.

The Western Conference finals begin Tuesday night at Golden State.

Ariza finished with 22 points and made six 3-pointers.

Every fan in the arena was given a red shirt emblazoned with the words “Clutch City” in yellow letters, bringing back the moniker of the 1994 and ‘95 teams that won back-to-back titles. These Rockets lived up to the nickname, winning their third straight game to become the first team to win a playoff series after trailing 3-1 since the Phoenix Suns did it in 2006 against the Lakers.

After taking a two-game lead after four games the Clippers looked destined to be heading to the conference finals for the first time in franchise history. But they failed in all three chances to put Houston away and are now left to ponder their collapse as they head home early yet again.

“It’s disappointing,” Griffin said. “We were close, but close doesn’t really count. Almost doesn’t count. We were up 3-1 and didn’t put them away. We can’t look at anybody but ourselves.”

Los Angeles never led, but tied it twice in the first 4 minutes. The Clippers insisted Saturday that they’d gotten over Thursday’s loss, but looked listless early in this one as Houston built the lead.

“I love my team,” Clippers coach Doc Rivers said. “I love the fact that they wanted to win so bad that, in my opinion, we almost couldn’t win. We have to fix that part. It requires great trust in each other. Our guys were trying to do it on their own.”

Little went right for the Clippers for most of the game and when a dunk by Jordan early in the fourth quarter simply bounced out of the rim, the big man could only look at the basket in disgust. The frustration was evident with Paul too, as he angrily threw the ball after picking up an offensive foul later in the fourth.

Harden was under the weather and on the bench in the fourth quarter when Josh Smith and Corey Brewer helped Houston outscore Los Angeles 51-20 to close out the win in Game 6. The MVP runner-up looked back to full strength on Sunday, scoring 12 points in the first quarter and finishing with eight assists and seven rebounds.

A 3-pointer by Jamal Crawford with about 2 1/2 minutes left in the third quarter cut the lead to eight points. Houston scored the next nine points, with five from Ariza, to push it to 83-66.

Pablo Prigioni grabbed two straight steals from Griffin in that span. Griffin fell to the court on the second one and shook his head as Prigioni darted away with the ball. Crawford made a layup for L.A. but Harden shook off Austin Rivers and stepped back for a jump shot near the buzzer to leave Houston up 85-68 entering the fourth.

The Clippers opened the second half with an 11-4 run, with five points from Paul, to get to 60-57 with 8 1/2 minutes left in the third quarter.

Harden got Houston going after that, driving into the lane and finishing with a one-handed dunk before dishing to Smith on the next possession and he swished a 3-pointer to make it 65-57.

The Rockets remained up by 8 midway through the quarter when Howard was called for a three second violation. But Griffin launched a bad pass that Prigioni snatched up and converted on the mistake with a 3-pointer to make it 70-59.

The Rockets led 56-46 at halftime.

QUOTABLE

Brewer on if the momentum of Game 6 carried over into Game 7: “It carried over a lot for us. It gave us our confidence back … we came out and jumped on them early.”

SAGER ATTENDS GAME

Longtime TNT sideline reporter Craig Sager, who is undergoing chemotherapy in Houston for leukemia, left the hospital between treatments to attend the game. Rivers greeted him at the end of his pregame media session, saying it was great to see him at a game.

TIP-INS

Clippers: Jordan had 16 points and 17 rebounds. … Crawford added 17 points.

Rockets: Howard had his 15th double-double in 18 career playoff games as a Rocket. … Smith finished with 15 points. The Rockets are 6-1 this postseason when he scores 10 or more points. … Rapper Nelly and NFL running back Adrian Peterson were among the celebrities in sellout crowd of 18,463.