"We just keep going 'til the clock says zero," said Iguodala, who scored six points in the fourth quarter.
Andre Miller added 16 points and seven assists, and Louis Williams had 17 points for the 76ers, 9-2 in their last 11. Elton Brand had 14 points, seven rebounds and a season-high six blocks in his third game back from a dislocated shoulder.
The Sixers improved to 13-8 under Coach Tony DiLeo, who replaced fired Maurice Cheeks on Dec. 13.
"It has to be one of the top victories," DiLeo said. "I really like coaching this team. Great attitude, great effort every night."
Tracy McGrady scored 24 points, and Luis Scola had 18 points and 10 rebounds for Houston. The Rockets have lost three of their last four, even as McGrady, Ron Artest and Yao Ming have finally gotten healthy.
The Rockets led 76-71 after three quarters and 82-75 with 9 minutes left. But Williams found Marreese Speights for an alley-oop dunk to trigger a quick 6-0 run that started the Rockets' collapse.
Miller's free throws with 3:29 to go broke an 89-all tie and Iguodala hit a long jumper just before the shot clock expired near the 2-minute mark to make it 93-89.
"We could've easily been out of that game, but we stuck to it," Miller said. "A few plays just fell our way. We just kept fighting. Andre hit some big shots down the stretch."
Yao drove for a layup with 56 seconds left, but Iguodala sank a tough shot from the baseline 20 seconds later to restore Philadelphia's four-point edge.
Yao flipped in a hook shot on Houston's next possession and got fouled by Samuel Dalembert. But Yao missed the free throw and the Sixers led 95-93 with 28 seconds left.
Iguodala missed a long jumper and the ball bounced out of bounds with 5.8 seconds remaining. The Rockets tried to run a pick-and-roll play with Yao, but Dalembert alertly switched and partially deflected McGrady's last-second 3-point try.
"I really don't have an answer," said McGrady, who went 8-for-20 from the field. "We just got to keep on grinding, keep digging and find an answer for it. We've got to be better, a lot better."
Philadelphia outrebounded Houston 48-40 and went 20-of-21 from the free-throw line to overcome 18 turnovers. The Sixers only committed four turnovers in the second half, a vast improvement from Monday night, when they gave away 22 turnovers in a 101-86 loss to New Orleans.
"First half (on Wednesday) was pretty much the same thing," Miller said. "But we only had like three or four in the second half, so that was a big part of the win."
Iguodala slammed home a spectacular alley-oop dunk over the 7-foot-6 Yao in the first quarter, giving the Sixers a 12-9 lead.
Artest came off the bench with 3:28 left in the quarter, the first time that McGrady, Yao and Artest had been on the floor together since Jan. 2. Artest and McGrady returned over the weekend from injuries, but Yao sat out the last two games with a sore knee.
The Rockets took advantage of the Sixers' sloppiness to build an eight-point lead late in the half. Philadelphia committed nine turnovers and shot 31 percent in the second quarter and Houston led 51-45 at the break.
McGrady sank two 3-pointers and dunked in the first 4½ minutes of the third quarter as the Rockets stretched the lead to 65-51. "It's a bad loss," McGrady said. "I feel that we played exceptionally well for three quarters."
The Rockets were up 73-61 after McGrady drove into the lane and dropped a pass to Scola for a basket. McGrady aggravated his wrapped left knee on the drive, limping back down the court, but stayed in the game.
The Sixers finished the quarter with a 9-3 burst, capped by Iguodala's pull-up jumper at the buzzer. Houston shot 36 percent (8-for-22) from the field in the fourth quarter to help fuel Philly's comeback.
Notes: The Sixers have won four straight games over the Rockets for the first time since a five-game streak between 1982-85. ... Philadelphia went 1-for-12 from 3-point range. ... The Rockets had a three-game home win streak snapped.
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