Rose contributed 18 points and 10 assists and reached double figures in assists for the first time this season. Reserve Larry Hughes had 16 points for the Bulls (8-9), who won for only the third time in 10 games on the road.
All three of Chicago's road wins came during this stretch.
"We got the ball in his hands in transition and he was finding guys," Bulls coach Vinny Del Negro said of Rose.
Rose entered the game averaging 5.8 assists, the best mark among rookies.
"I'm feeling good and taking it game by game," said Rose, who played a team-high 40 minutes. "We're moving the ball and finding the open person. We're playing team basketball and that's what it's all about."
Philadelphia scored a season-low 78 points in a 24-point loss at Boston on Friday and has been held below the 100-point mark in seven consecutive games.
"We've got to step it up," Brand said. "We've lost two games in a row where the other team has taken it to us."
The Bulls held a 71-66 lead late in the third before running off 12 straight points to take an 83-66 advantage at the end of the quarter. Rose had six of the 12 points, including a high-flying, one-handed dunk with 32 seconds remaining.
"I think by us spreading out the basketball the way we did, we were really consistent with our effort in the zone and we got in transition," Del Negro said.
After a 3-pointer by Hughes gave the Bulls a 92-73 lead with 7:21 left, the fans booed and a large throng of them began to vacate the arena. When the game ended, the boos careened down once again.
"We have to get ourselves back in the mind-set of defending," Sixers coach Maurice Cheeks said.
The Sixers led by as many as 15 points in the first half before Chicago went on a 14-0 run to cut the lead to 41-40 on a basket by Luol Deng with 4:57 remaining.
Philadelphia finished the half strong and held what would wind up being a short-lived 55-52 lead.
Brand was originally selected by Chicago with the top pick in the 1999 draft. Brand spent two seasons with the Bulls and seven with the Los Angeles Clippers before signing with the Sixers as a free agent in July. Young had 11 points in the first quarter for the Sixers. The announced crowd was 13,561, but there were pockets of empty seats throughout the 20,000-plus seat arena.