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.

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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 three-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.”

Blake Griffin scored five points in a 9-0 run to cut the lead to eight points with less than 2½ minutes remaining. Harden made two free throws after that, but a dunk by DeAndre Jordan got the Clippers within eight again. This time, Trevor Ariza hit a three from the corner to secure the victory.

Howard was nervous until Ariza hit the final three.

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