The Bulls, who are now 5-1 for the season, led by 17 at one stage before holding out for a 107-99 win.
The Jazz, defending the last remaining unbeaten NBA record, had made their best start to a season since 2006-07.
Zach LaVine, playing despite a thumb sprain, added 26 points for the Bulls and Nikola Vucevic added 16 points and 12 rebounds.
Reigning champions the Milwaukee Bucks were beaten 102-93 by the San Antonio Spurs, who recorded their first away victory of the season.
