Chris Paul gives Clippers the gift of his presence in Game 3

Chris Paul promised he would play if he could, shedding the haute couture for his preferred evening wear.

He didn’t just put on his uniform again Friday night at Staples Center. He wore out the Houston Rockets.

Paul flipped passes and drew defenders and defied the injury odds, his impact far exceeding his modest statistics on an evening the Clippers needed their point guard’s grit before the game became a runaway.

Six days after he played through a strained left hamstring to hit a game-winning shot on his home court, Paul returned to put on a performance that was every bit as gutsy during the Clippers’ 124-99 victory in Game 3 of the Western Conference semifinals.

“If I could give anything to help the team, I wanted to do it,” Paul said. “I got through it.”

Paul more than persevered, his toughness best illustrated early in the third quarter when he reached down to rip the ball out of Terrence Jones’ hands as the Rockets forward laid on the court during a break in the game.

So what if it was a dead ball? Paul just wanted to quickly inbound the ball.

Most Clippers possessions ended favorably with Paul on the court. He finished with 12 points and seven assists in 23 hold-your-breath minutes, and so what if he made only five of 12 shots? His presence helped his team get the second of the four victories it needs to reach the conference finals for the first time in franchise history.

Paul also lent both hands when understudy Austin Rivers went on an unexpected scoring barrage in the third quarter, playfully pounding the backup point guard on the chest as the Clippers scored 18 consecutive points. Paul had to play only 73 seconds in a fourth quarter that turned into one long celebration as the Clippers led by as many as 32 points.

The Clippers are learning that if the San Antonio Spurs were Beethoven’s Ninth Symphony, all precision and purpose, the Rockets are a mommy-and-me singalong, a cacophonous collection of notes that often don’t go together.

Paul was pleased to experience it himself in his first game action since he made the now-legendary one-handed, one-legged running jumper with one second left to beat the Spurs in Game 7 of the first round.

He spent the first two games of the conference semifinals in a sports coat and a suit as his teammates stole one game in Houston and sputtered to defeat in the other.

“It’s actually harder sitting out,” Paul said. “I was stressed out sitting out Game 1 and Game 2, so it was fun to be out there and be part of the action.”

Paul moved gingerly from the opening tip Friday, but there was nothing halting about his game. He came out assertive, firing a three-pointer that missed on the Clippers’ first possession and watching a mid-range jumper roll out of the rim shortly thereafter.

Paul shrugged and went into assist mode as if it was time for another State Farm ad. He showed he still had the touch on the pick and roll, feeding Blake Griffin with a pair of passes that resulted in vicious dunks. Then came two assists to J.J. Redick and one more to Griffin and suddenly Paul was on an assist-per-minute pace.

“I thought his passing in the beginning of the game set the tone for us,” Clippers Coach Doc Rivers said.

Paul then got his jumper going, making back-to-back 15-footers before leaving the game with the crowd roaring and his team leading by four points. Clippers Coach Doc Rivers subbed son Austin in for Paul with 61/2 minutes left in the first quarter, far earlier than Rivers usually removes Paul.

Paul’s minutes restriction meant he was part of some odd rotation pairings, starting the second quarter alongside Spencer Hawes, Glen Davis, Rivers and Jamal Crawford. Paul made that work too in helping the Clippers push their advantage into double figures.

One of Paul’s final hurdles in being cleared was going up against former Rocket Sam Cassell, the 45-year-old Clippers assistant coach whose job duties now include confidence-building.

“My guess is he scored every time,” Rivers joked of Paul before the game.

Turning serious, Rivers said the Clippers pushed Paul to make sure he was capable of enduring an NBA playoff game. Not that Rivers wouldn’t be sweating Paul’s every step come tipoff.

“This injury is just one of those injuries that scares the hell out of me,” Rivers said. “I think our trainers are more comfortable with it.”

Paul walked with a slight hitch in his step as he went through the layup line about 20 minutes before the game.

Even Rivers was unsure what to expect. Would Paul be his aggressive self? Would he play tentatively? The coach said it was his job to watch and adjust as needed.

It turned out the only thing he needed to do was let Paul play.

ben.bolch@latimes.com

Twitter: @latbbolch