All-Star Blake Griffin went down with back spasms in the first quarter and when Glen Davis threw a temper tantrum early in the second, they were trailing by 13 points.
But instead of crumbling, the Clippers rose to the challenge as Chris Paul got hot and helped Los Angeles erase the deficit by halftime and hold on for the 118-107 win.
Paul had 30 points and 12 assists and Jamal Crawford added 22 points to help the Clippers clinch their franchise-record third straight playoff appearance.
James Harden led the Rockets with 32 points, and Chandler Parsons had 28. DeAndre Jordan added 20 points, 12 rebounds and six blocks for the Clippers, who swept Houston this season and are third in the Western Conference.