Thaddeus Young paced the Sixers (22-16) with 17 points. Jrue Holiday added 16, and Iguodala and Brand scored 14. Brand led the team with 13 rebounds.
Joakim Noah had 18 rebounds and 11 points for the Bulls (31-8), and Carlos Boozer scored 11.
Down by as many as eight points in the second quarter, the Bulls used a 15-4 run to begin the fourth quarter and take an 81-68 lead with 7 minutes, 52 seconds to play.
But the Sixers needed less than three minutes to get back into it, using a 10-1 run to pull to within 82-78 on Holiday's breakaway slam dunk with 5:28 to play.
After two Chicago buckets pushed the Bulls' lead to 87-78, the Sixers scored seven straight ending with a Young layup to make it 87-85 and force the Bulls to call a timeout.
After an air ball by Iguodala and a missed jumper by Young, Rose took matters into his own hands at the other end, hitting a running jumper near the basket that gave the Bulls a 93-89 advantage and forced the Sixers to call timeout with 20.2 seconds to play.
When play resumed, Brand was called for a moving screen, denying the Sixers a shot and giving the Bulls the ball with 19 seconds to play.
When the Sixers beat the Bulls in their last meeting, Chicago had role players Kyle Korver and Ronnie Brewer in the starting lineup instead of Richard Hamilton and Luol Deng.
But the Sixers also were down a starter, playing without center Spencer Hawes, who is expected to begin basketball activities Monday before returning later this month.
What keyed that Sixers victory then more than anything was the team's forcing the Bulls into 29 turnovers that resulted in 29 points.
If a team is going to have any success against the Bulls, it has to at least slow down Rose.
Rose scored 13 points in the first quarter on 5-of-8 shooting and helped the Bulls out to a 26-24 lead going into the second.
But the Sixers limited Rose to just one more field goal the rest of the half, and that didn't come until he nailed a step-back 22-footer under duress to end the half.
The Bulls needed Rose's bucket dearly at that point because the Sixers' defense had limited the Bulls to just 12 points to that point.
The Sixers didn't shoot very well in the second quarter either (8 for 24). However, they still managed to go up by eight points when Iguodala split a pair of free throws with 2 minutes, 50 seconds to play in the second quarter.
Shortly thereafter, Rose nailed his bucket to pull the Bulls to within 46-40 heading into the second half.
Contact staff writer John N. Mitchell at firstname.lastname@example.org or @JmitchInquirer on Twitter.