Andres Nocioni added 20 points and Tyrus Thomas had 16 points and 12 rebounds for Chicago in the game played at the Assembly Hall on the University of Illinois campus.
Luol Deng and No. 1 overall draft pick Derrick Rose both had 14 points for the Bulls (1-3).
Carlos Boozer was 8-for-12 from the field and finished with 21 points for the Jazz (2-3). Mehmet Okur scored 17 points and Paul Millsap added 16 for Utah, which led 52-47 at halftime.
Gordon scored five of the Bulls' final seven points, including a three-point play with 1:27 left that put Chicago ahead for good. The Bulls outscored the Jazz 29-19 in the fourth quarter.
"I don't think (Gordon) knows the offense very well, but he's just picked up things fast. I just tried to put him in pick-and-roll situations, real basic stuff where he could be aggressive," first-year Bulls coach Vinny Del Negro said. "Ben can make shots and when you can put the ball in the basket it brings another dimension."
Deron Williams, who led Illinois to the national championship game in 2005, had 14 points and nine assists for the Jazz, while Ronnie Brewer added 11 points.
Williams said the game didn't remind him of college, despite a vocal and supportive crowd.
"I didn't have to go to class before the game," he said.
The Bulls trailed by as many as 13 points in the second quarter before chipping away at the deficit from the free throw line, going 11-of-11 in the period.
Rose left the game with a leg cramp in the third quarter.
It was the first time the Bulls have played in Champaign since a 1989 preseason game featuring Michael Jordan. Jordan's son, Jeffrey, is a sophomore walk-on guard for the Illini and was in attendance Friday night.