Bledsoe and Griffin added 19 points apiece for the Clippers, and Matt Barnes had 18. Bledsoe's points were a season high and Green also had a season high with 15 points.
Crawford said the win was a perfect example of the way they want to play.
"That's what it's about. We do it collectively," he said. "We all pull for each other and we're all in it together and that's how we win."
Crawford had a spectacular run to start the fourth quarter where he made five straight shots, including a pair of 3-pointers to push the lead to 102-82. Houston called a timeout after his last bucket in that run and DeAndre Jordan dashed off the bench and met him for a celebratory jump and bump near center court.
The Rockets went on a 10-2 run later in the fourth quarter to pull to 108-96. But The Clippers responded with two 3-pointers sandwiched around a basket by Jeremy Lin to thwart the comeback attempt.
Harden was disappointed that the Rockets didn't get back on track in their one home game before four straight on the road.
"You can't do that, especially coming off a three-game road trip, a three-game losing streak," he said. "We've got to be better, especially on the defensive end. We've got to guard in order to win games. It's simple."
The Clippers were up by one point in the second quarter when Lamar Odom received his third foul. Del Negro received a technical for arguing the call and seconds later Odom was also giving a technical for arguing. Harden made just one of the two free throws, but Morris connected on a 3-pointer a few seconds later to give Houston a 39-36 lead.
Houston trailed by two about a minute later before using a 13-4 run to go on top 52-45 about 3½ minutes before halftime. Los Angeles outscored the Rockets 13-7 for the rest of the quarter to cut the lead to 59-58 at halftime.
Parsons finished with 17 points and Lin added 12 points with 10 assists.
NOTES: Tuesday was Hill's 1,000th career game, making him the 20th active player to reach the mark. ... Houston Texans stars Arian Foster and Andre Johnson watched the game from courtside seats. Foster received a nice ovation from the crowd as he walked alongside the court to his seat in the third quarter. The Texans lost to New England in the divisional round of the NFL playoffs on Sunday.