Chicago made it close in the final six minutes, cutting a 25-point fourth-quarter deficit to eight, but the Heat held them off for a 107-95 victory.
Miami followed its ring ceremony with a lethargic start.
Udonis Haslem slammed home the game's first basket before Chicago reeled off nine straight points.
Chicago led 13-10 when Battier and Allen entered the game with 3:52 left in the first quarter. Each hit a 3-pointer as Miami closed with a 7-2 run to lead by two heading into the second quarter.
The entire Heat team then raised the intensity of its defense, getting some easy baskets, and moved the ball better offensively.
Battier scored eight points in just under seven minutes, and Allen had five assists in 9:04 of the quarter.
Cole (5 points, four rebounds) and Andersen (2 points, three rebounds) also helped fuel Miami's second-quarter surge. The Heat outscored the
Bulls 37-18 in the quarter to lead 54-33 at halftime.
The Bulls shot 30 percent (6 of 20) and committed six turnovers in the second quarter. Chicago forward
Luol Deng committed three fouls in the first quarter and didn't play in the second.
Bulls point guard
Derrick Rose had 12 points and four assists in 34:21 as he returned after missing all of last season due to a knee injury.
Center Greg Oden and guard Roger Mason Jr. were designated as Miami's inactives and watched the game in street clothes.
The turning point
Miami dominated the second quarter to build a 21-point halftime lead.
They did so behind bench contributions and despite Wade (2 of 8) and Bosh (3 of 8) struggling through the first 24 minutes.
The difference maker
Shane Battier. The reserve forward entered with Allen late in the first quarter and helped produce a much-needed spark. Battier hit all four shots, including three 3-pointers, in the first half to take a team-high 11 points into the locker room as Miami led 54-33.
Stat of the game
Miami shot 55 percent (11 of 20) from 3-point territory. Chicago hit 7 of 26 (26.9 percent).
Must see video
Heat visit the Philadelphia 76ers at 7 p.m. Wednesday.