Seven players scored in double figures for Philadelphia, which has won two straight since learning that Brand will have season-ending shoulder surgery Monday.
"Talk about a team win," coach Tony DiLeo said. "Everyone contributed. That's the way our team is. Everyone on the bench cheers for everyone on the court no matter if they're starters on the bench or if our subs are on the bench."
The Sixers are 12-8 without Brand, who signed a five-year, $80 million deal last summer. That's an encouraging sign for a team hoping to make a strong playoff push and get the No. 4 spot in the Eastern Conference that ensures home-court advantage in the first round.
They'll try to move two games above .500 for the first time this season when they host Phoenix on Monday. Another 41 points from the bench will help.
"As a group, we haven't had the best couple weeks," said Louis Williams, who chipped in with 10 points. "To have a fourth quarter like tonight, the guys are really excited."
Miami has lost four of five. The Heat are one game ahead of Philadelphia for the sixth spot in the East. The four teams jostling for the No. 4 seed are separated by 3 1/2 games.
"Their bench changed the game," Heat coach Erik Spoelstra said.
The Sixers trailed most of the second half until Ivey's layup off a terrific pass by Speights gave them a 74-73 lead early in the fourth.
After Wade missed one of two free throws, Chalmers missed a pair. Then, Williams made two free throws and Ivey nailed a 3-pointer from the baseline to put the Sixers ahead 79-74.
Speights rejected Wade at the opposite end, and Thaddeus Young hit another 3 from the baseline. Following a timeout, Ivey intercepted a pass and scored on a fast-break layup to make it 84-74 and cap a 23-5 run.
The teams traded a few baskets before Ivey drilled another 3 for an 89-78 lead with 3:30 left. The Heat didn't get much closer the rest of the way.
"It was winning time and they made the plays and we didn't," said Wade, who was fighting the flu.
Wade and Chalmers combined for 19 of Miami's 25 points in the third quarter, helping the Heat take a 69-63 lead. Chalmers hit a long jumper and Wade followed with another long one to put Miami up 63-55, and the duo scored the Heat's final 10 points.
The Sixers missed 14 of their 18 shots in the third, but made all 11 free throws to stay close.
Then, DiLeo turned to his bench in the fourth.
"Our energy guys came in and did a fantastic job," DiLeo said. "They really wore them down down the stretch."
Ivey not only scored 10 points in the fourth quarter, but helped shut down Wade. The NBA's leading scorer had one point in the final 12 minutes.
"Coach emphasized we were lackluster in the first half, giving up a lot of layups," Ivey said. "We needed a boost. The second unit came in and gave us energy."
The biggest lead of the first half was 7-0 as the Sixers came out strong. It was 44-44 at halftime.
Philadelphia is 16-10 since Tony DiLeo replaced Maurice Cheeks as coach. ... The Heat have lost five straight in Philly. ... The Sixers improved to 3-2 during their season-long seven-game homestand. They don't play on the road again until Feb. 17 at Indiana.