Houston Rockets kept doubts at bay in series comeback over Clippers

Doubt could have seeped into the minds of every one of the Houston Rockets when they were faced with a monumental task.

To be honest, perhaps the Rockets should have doubted themselves when they were down 3-1 in the second-round playoff series to the Clippers. Maybe they should’ve when they were in a 19-point hole during Game 6 in Los Angeles.

But these Rockets refused to succumb to doubts, pulling themselves up from the depths to make some NBA history after beating the Clippers, 113-100, in Game 7 Sunday at the Toyota Center.

After they had advanced to the conference finals for the first time since 1997, all of the Rockets maintained they had remained self-assured despite the mountain they had to climb.

“It’s easy to doubt when you’re down 19 on the road,” said James Harden, who had 31 points, eight assists and seven rebounds. “It’s easy to give in and say, ‘Maybe next year.’ I think the injuries this year, throughout the entire whole year, kind of made us fight through adversity no matter what.

“We always had to find a way to through it, find a way to fight — and another case was being down 3-1. We just had to take it one game at a time and not look at the bigger picture.”

Only eight teams had ever come back from a 3-1 deficit to win an NBA playoff series.

But the Rockets became the ninth, the first team to make that comeback since the 2006 Phoenix Suns did the same thing to the Lakers.

The Rockets’ franchise actually has a history of overcoming 3-1 deficits in the playoffs. The 1995 team did it against the Phoenix Suns. The current team’s feat puts it with the Boston Celtics as the only franchises to have done it twice. Now the Rockets will meet the Golden State Warriors in the conference finals Tuesday in Oakland.

“There were times where we very frustrated with each other and the way that we represented ourselves as a team,” said Dwight Howard, who had 16 points and 15 rebounds. “But I don’t think there was any doubt on anybody’s mind and hearts that we could win. I think that’s what carried us over for the rest of the series.”

Once the Rockets tied the series at 3-3, the odds turned in their favor of doing the improbable.

In a Game 7 of the NBA playoffs, the home team had won 80% of the time, going 96-24.

Houston pushed it to 97-24 by winning the last three games by an average of 15.3 points per game.

They got contributions in Game 7 from players like Trevor Ariza (22 points, 7 rebounds), Josh Smith (15 points) and Corey Brewer (11 points) to show that perhaps they really didn’t doubt themselves.

“Like I said last time, we had every opportunity to give up,” Howard said. “We continued to fight, continued to trust each other. We showed a lot of composure and a lot of character in the team. That was a good win against a great team.”

broderick.turner@latimes.com

Twitter: @BA_Turner