James Harden scored 31 points, and Dwight Howard had 16 points and 15 rebounds as Houston became just the ninth team in NBA history to overcome a 3-1 deficit to win a play-off series.
The Rockets needed an epic comeback in Game 6 to overcome a 19-point third-quarter deficit and force Game 7.
No such heroics were needed Sunday when they were up by 17 after three quarters and Howard opened the fourth quarter with a 3-point play to push it to 88-68.
Blake Griffin scored five points in a 9-0 run to cut the lead to eight points with less than two and a half minutes remaining.
Harden made a pair of free throws after that, but a dunk by DeAndre Jordan got the Clippers within eight again.
But Trevor Ariza hit a 3 from the corner to secure the victory as he finished with 22 points, including six 3-pointers.
Griffin had 27 points and Chris Paul had 26 points and 10 assists for the Clippers, who knocked out the defending-champion San Antonio Spurs in the last round.
After taking a two-game lead after four games the Clippers looked destined to be heading to the conference finals for the first time in franchise history.
But they failed in all three chances to put Houston away and are now left to ponder their collapse as they head home early yet again.
The Western Conference finals begin Tuesday night against No 1 seed the Golden State Warriors.??