Crawford had 16 points, Chris Paul added 14 points and 13 assists and DeAndre Jordan had 12 points and 18 rebounds for the Clippers. Griffin also had seven rebounds and Redick shot 8 for 15 from the field. Darren Collison added 10 points off the bench.
Los Angeles trailed 71-60 with about 5 minutes to go in the third quarter before its big run that lasted into the opening minutes of the fourth.
"I kept telling them to hang in there," Clippers coach Doc Rivers said. "We hung around and got it going and our defense won the game. Houston had, I think five points in the last six minutes (of the third quarter), and 37 points in the whole second half for a good offensive team. I thought Darren Collison was fantastic and Jamal made big shots."
Los Angeles shot 14 for 23 on free throws, but just 9 for 24 on 3-pointers.
James Harden, who was a game-time decision with a bruised left foot, had 12 points on 4-for-15 shooting.
Houston finished 17 of 27 from the free throw line.
Trailing by 11, the Clippers scored the final 13 points of the third quarter to take a two-point lead on a tip-in by Crawford at the buzzer.
"We were on the line trying to get it to 13, and then it just snowballed from there," Houston coach Kevin McHale said about the end of the third quarter. "We missed some shots, and we started doubting it and we stopped taking some shots that we needed to take. Then, we got a lot of turnovers and we just got really passive. We just got nothing going from that point on."
Los Angeles kept the run going to start the fourth, with Crawford capping it with a three-point play with 10:21 remaining in the game to increase the lead to 78-71. Crawford had seven points and Jared Dudley added five points in the spurt that lasted nearly seven minutes.
"Chris got it started being a spark plug for us," Crawford said about what changed in the third. "I think it was kind of slow to start the game, and we just followed the lead and coach kept challenging us to get defensive stops because that breaks a team's spirits. Our offense was coming from our defense."
Paul pointed to the Clippers' defensive intensity as a reason for the run.
"We knew that this was a team that made some runs, but at the same time, they will let you back into the game," Paul said. "Once we started the third quarter, we came out and played with a lot more purpose, more passion. That tip in by Jamal at the end of the third quarter was huge for us."
Houston pulled to 84-80 on Harden's three-point play with 7:21 remaining, but that would be as close as they would get.
Los Angeles had a 9-3 run over the next three minutes to increase the advantage to 92-83 on Griffin's free throw with 4:15 to go.
Houston tried a `Hack a Jordan' tactic with 3 minutes remaining, and despite Jordan missing both free throws, Los Angeles countered by fouling Howard and taking Jordan out of the game. Howard made a free throw to get the Rockets to 97-90, but Redick hit two free throws and Collison made a 3-pointer with 1:39 remaining to stretch the lead to 102-90.
Los Angeles outscored the Rockets 27-16 in the third quarter and 61-39 in the second half.
"We just stopped playing the way we had played to get the lead, and when you are playing against a team like the Clippers, they've been together a couple of years and play well together," Howard said. "We had to continue to do things that got us the lead, and we didn't do that tonight and they capitalized on it. They got a good road win."
The Clippers opened up an 18-8 lead midway through the first quarter as Redick scored eight of Los Angeles' first 10 points. Houston finished the quarter on an 11-0 run over the final 3:40 of the period. Howard had 10 points in the first, including the first four of the run.
Houston kept it up in the second quarter, extending the lead to 10 at 39-29 on back-to-back 3-pointers by Beverley with 7:26 left in the period.
The Rockets led 55-46 at halftime.
Los Angeles F Matt Barnes missed his third straight game with a right thigh contusion. ... Beverley had a career-high four steals. ... The Sandau Trio Russian Bar, who were on "America's Got Talent," performed at halftime.