Amir Johnson also finished 23 points, including four three-pointers, to help the Celtics avenge their lone loss of the season.
Boston played without center Al Horford, who was placed in the concussion protocol Tuesday after exhibiting concussive symptoms during practice.
Johnson helped pick up the slack without him, scoring 16 points in the third quarter. The Bulls managed just 18 points in the period, their lowest scoring quarter of the season.
The Bulls cut into what had been a 16-point Boston lead in the fourth quarter and tied it at 100 on two free throws by Nikola Mirotic. But Boston regained the lead 101-100, then went up five on a driving layup by Thomas and basket by Marcus Smart.
Jimmy Butler led Chicago with 23 points and nine rebounds.
Before Wednesday Johnson had never made more than two three-pointers in a game and had never attempted more than four. He entered the night 0 for 1 on the season.
Boston led by as many as 14 points in the first half, but took only a two-point lead into halftime.
After a slow start, Jae Crowder scored eight straight points during a 21-4 Boston run. The Bulls stayed in it via a few mini spurts, including an 8-0 run by Butler.
Bulls: G Michael Carter-Williams (left knee bruise, left wrist sprain) and Doug McDermott (concussion) both sat out. Coach Fred Hoiberg said McDermott felt good, but that he hadn't gone 24 hours without experiencing symptoms yet.
The Celtics' 36 points in the first quarter was the most in a period for Boston this season. Its previous high was 33.
Bulls: Host the Knicks on Friday night in Derrick Rose's first game back in Chicago since being traded to New York this offseason.
Celtics: Head to Cleveland on Thursday for their first matchup of the season against the defending champions.