HOUSTON (AP) -- Luther Head was never shy about taking clutch shots in college and he's still not afraid to take them in the pros.
Elton Brand scored a season-high 37 points for Los Angeles and drove for a dunk with 1:01 left that put the Clippers up 105-104.
Yao was whistled for an offensive foul barreling down the lane, but Brand missed a shot from the wing to give Houston another chance.
Tracy McGrady, who led the Rockets with 21, drew the defense to him and found Head wide open in the corner for the go-ahead 3-pointer.
Head came into the game shooting 44 percent from 3-point range in the fourth quarter and during a late timeout, Houston coach Jeff Van Gundy told Head to be ready in case McGrady got into trouble.
"Whenever your coach has confidence in you, it just puts confidence in yourself," Head said. "That's why I love playing for the guy. When he trusts you, he usually shows that he trusts you."
Head finished his college career as Illinois' 19th leading scorer and its fourth-best 3-point shooter.
"My coach in college (Bruce Weber) said I had a lot of confidence in taking the last shot," Head said. "I don't know. I just don't get excited about much. Maybe that's the thing."
The Clippers had one more chance to tie it after Head's shot.
After a timeout, Brand tried to find Corey Maggette cutting to the basket, but Yao batted the ball to Rafer Alston, who raced down the floor and was fouled with 5.9 seconds remaining. Alston hit the free throws and finished with 20 points.
"I am very disappointed we couldn't get the win," Brand said. "We had too many turnovers late in the game."
Brand also had 10 rebounds to get his 29th double-double of the season. Chris Kaman added 16 for the Clippers, who've lost five in a row and six of their past seven.
The loss was costly -- the Clippers fell out of the eighth playoff spot in the West, and are percentage points behind Golden State.
"It's satisfying to play well, but we have to get victories," Brand said. "We had opportunities and we just didn't finish. We just wanted to win this game so badly and we let it slip away. It's a tough loss."
Chuck Hayes added 16 points for the Rockets, who've won four of their past five and 13 of their past 16 meetings with the Clippers.
The Rockets nearly blew a big advantage after building a 17-point lead in the first half.
"It went three ways," Alston said. "It started as a blowout win, then went almost to a devastating loss, and then into a nail-biting win."
The Clippers missed 10 of their first 11 shots and trailed 25-9 eight minutes into the game. The Rockets hit 9 of their first 11 shots.
Hayes, Houston's power forward, had 10 points in the first quarter, reaching double digits for the fourth time in five games.
The Clippers regrouped and shot much better in the second quarter, hitting 11 of 20 shots. Cuttino Mobley had eight points in the quarter to lead the comeback and Brand hit two free throws to cut the deficit to 57-52 by halftime.
Alston and McGrady opened the third quarter with 3-pointers to stretch the lead to 11. Both teams played a sloppy quarter from there, with wild passes and missed shots. McGrady did have one highlight-reel play, a behind-the-back assist to Hayes for a layup.
The Rockets headed into the final quarter with an 87-76 lead.
Brand scored 12 points in the third quarter and swished back-to-back jumpers from the wing over the 7-foot-6 Yao early in the fourth to trim Houston's lead to 93-88.
Yao scored with 7:18 remaining, but Hayes, the Rockets' second-leading scorer to that point, fouled out trying to guard Brand. Daniel Ewing then made a 3-pointer to draw the Clippers within four.
Maggette turned a steal into a fast-break layup and a three-point play to give Los Angeles its first lead at 99-96. The teams traded baskets over the next few minutes before Head's clutch shot put the Rockets ahead for good.
"He's been knocking those shots down pretty much all season," McGrady said. "He is one guy who seems to always be open in situations like that."
Yao had only 14 points in his sixth game back from a broken leg. He cracked his right tibial plateau in the first quarter against the Clippers on Dec. 26.
Brand became the Clippers' leading rebounder, passing Loy Vaught. Brand now has 4,478 rebounds, surpassing Vaught's 4,471. ... The Rockets are 8-2 in games following double-digit losses this season. They lost 103-82 in Phoenix on Monday. ... Former Rocket Sam Cassell missed his second straight game with an abdominal strain.