The Clippers entered the fourth quarter down 10 points, 84-74, but they scrapped and clawed their way back, tying the game at 96 with just over three minutes left after Chris Paul made a three-pointer.
Terrence Jones responded with another three-pointer, then Matt Barnes made a layup. With 12 seconds left and the Clippers down, 99-98, Griffin dribbled the ball across the half-court line, and got called for a charging foul against Trevor Ariza as he penetrated the lane.
James Harden then made one of two free throws with 8.9 seconds left to put the Rockets up by two, and Paul missed his chance to tie the game with 1.2 seconds left, falling short on a fade-away jumper.
Paul led the Clippers with 23 points, though it took him 21 shots to get them. Barnes had 19 points on seven-for-12 shooting, including making five three-pointers. J.J. Redick added 15 points.
Griffin, who returned to the court Sunday after missing 15 games because of a staph infection in his right elbow that required surgery Feb. 9, had 11 points on four-for-10 shooting and 11 rebounds in just under 41 minutes of play. Griffin even had a slam dunk in the fourth quarter, but it was waived off because of a charge on Barnes.
The Clippers outshot the Rockets from the field, 43.9% to 37.2%, and from beyond the three-point line, 46.2% to 23.3%, but they had 20 turnovers compared to Houston's 13. The Rockets, however, made 29 free throws, more than the Clippers even attempted (24).
Harden, who averaged 15.3 points in his team's last three games against the Clippers this season, had 24 points in the first half of Sunday's game, finishing with a game-high 34 points, seven assists and seven rebounds.
Reserve guard Nate Robinson was a spark plug for the Clippers in the fourth quarter, diving for loose balls, spending quite a bit of time rolling on the floor. He hit a big three-pointer at the top of the fourth quarter to cut the Clippers' deficit to three, 86-83, and finished with seven points.
The Clippers were playing without reigning sixth man of the year Jamal Crawford, who is out with a right calf contusion. There was another injury Sunday -- Jordan Hamilton sustained a right ankle sprain in the third quarter and did not return to the game.
With the Rockets' win, the teams split their season series.
The Clippers (42-25) remain in fifth place in the Western Conference, falling 2 1/2 games behind the fourth-place Rockets (44-22).