Ron Artest scored 19 points and Yao grabbed 10 rebounds and went 12-for-13 from the free throw line for the Rockets, who played their fourth straight game without McGrady. The seven-time All-Star is out three weeks with a sore left knee.
The Rockets overcame poor shooting from the field by going 31-for-39 from the foul line -- 12-for-14 in the last six minutes -- to beat the Clippers for the seventh straight time.
"That's great when guys step up, because the only way you're going to win is with the team," said Artest, who made only five of 15 shots but went 6-for-7 from the line. "We've just got to play the right way."
Houston had four players in double figures, a recipe for success until McGrady, its second-leading scorer and top playmaker returns. The Rockets had six double-figure scorers in Saturday's 103-84 win over San Antonio, their second game without their star.
"In this three weeks, we need a little bit more from everybody," Yao said. "He is a big part of our team. I think that everybody understands that, and everybody is clear that when we step on the court, we need to really be ready to play."
Baron Davis had 13 points and nine assists, despite leaving in the first quarter with apparent food poisoning. He started the second half and never came out of the game again, playing 34 minutes in all.
"I must have ate something before the game and it didn't want to come down or out," Davis said. "I thought if I sat down in the second half, I couldn't have continued. I tried to do something to help my teammates. It just wasn't enough."
The Rockets led most of the way, but Thornton flew in for a dunk with 3:23 left to cut the lead to 95-89.
Yao, guarded by the shorter Randolph most of the game, flipped in a turnaround 20 seconds later and Houston put away the game from the line. The Rockets came in shooting 76.7 percent from the line and the 31 makes in 39 attempts were both season highs.
"That's remarkable whenever a team gets to the line that many times," said Alston, who went 4-for-6 on free throws.
Yao hit his first two shots, but the rest of the Rockets missed 12 of their first 15. Yao also started 8-for-8 from the line to help Houston build an early lead.
Randolph struggled to guard Yao and when the Rockets' center wasn't taking point-blank shots, he was getting swarmed by the Clippers and going to the free-throw line.
"At the beginning of the game, I tried to get a quick score and make them come to double-team me," Yao said. "I know they have a couple of big guys, so we can make some pressure inside."
But Houston had its own problems controlling Randolph, who scored 18 in the first half. The Rockets continued to shoot poorly from the field in the second quarter, but led 53-46 at the break after going 17-for-21 from the line.
Davis started the third quarter, but Artest and Alston sank consecutive 3-pointers and the Rockets quickly pushed their lead to 15.
The Clippers answered with a 9-0 run to trim the deficit back to six. Later in the quarter, Davis sank a 3-pointer and Randolph scored inside to pull Los Angeles to within two.
Davis had five assists and the Clippers shot 60 percent (12-of-20) in the third quarter to trail only 77-76. Carl Landry and Shane Battier scored inside on consecutive trips early in the fourth to extend Houston's lead again.
"It's tough playing uphill and trying to come back," Thornton said. "Down the stretch, Houston executed, like good teams do."
The Rockets led 87-83 when Yao returned after a rest with 6:07 remaining, and Houston never lost the lead.
Houston has won 19 of the last 22 meetings with the Clippers. ... Clippers C Chris Kaman sat out for the third straight game with a strained left arch. Coach Mike Dunleavy said that Kaman would probably miss "another week to 10 days." ... Rockets G Steve Francis was activated for the first time this season, but did not play. ... The Clippers are off to their worst start since opening the 1998-99 season with 17 straight losses.
Blake Griffin surprised by reduced role
Blake Griffin says he wasn't expecting to be completely removed from the Nets' rotation.
Why taking Kemba Walker out of the rotation could be a risk for Knicks
Ramona Shelburne dives into the risk and reward of Tom Thibodeau removing Kemba Walker from the starting lineup.
Updated fantasy basketball head-to-head categories rankings
Eric Karabell ranks the top 200 players in head-to-head categories leagues, with LaMelo Ball taking a spot in the top 5.