Mario Chalmers added 16 points and six assists for the Heat, who have won four in a row. Udonis Haslem tied a season-high with 14 rebounds and Shawn Marion hauled in 10 boards for Miami, which surpassed last season's win total with its 16th triumph.
Ben Gordon logged 15 points and Aaron Gray set season-highs with 12 points and 11 rebounds for the Bulls, who have dropped six straight on the road and two in a row overall.
Luol Deng had eight points and nine rebounds before leaving with 7:52 left in the third after rolling his left ankle coming down after a rebound. He was taken to the locker room for X-rays and did not return.
With the score tied at 64 heading into the fourth, Daequan Cook's three- pointer put Miami up 71-67 with 8:51 left in regulation.
Two free throws from Derrick Rose brought the visitors within 73-71, but Cook drained a three-pointer for a five-point lead.
Moments later, Cook sank a trey to give the Heat an 81-73 advantage with 5:49 left in the game.
Miami went up 86-73 following Haslem's two free throws with 4:46 remaining, and Chicago failed to get within single digits the rest of the way.
The Bulls edged the Heat for a 21-18 lead after the first stanza and increased their cushion to 45-40 at the half.
The teams traded baskets and a Chalmers bank shot tied it up at 56 with just over five minutes left in the third frame.
It went back and forth and the score was still even, 64-64, heading into the final 12 minutes.