Nate Robinson added 18 points for the Bulls, who rebounded nicely from a 32-point loss in Denver 24 hours earlier.
Al Jefferson had a season-high 32 points for Utah, scoring the first eight in the fourth period to give the Jazz a 77-73 lead.
Boozer, plagued by foul trouble early, got rolling with about 5 minutes remaining against his former team. His layup tied it at 83 with 2:29 left and he scored the next five from the free throw line, including a pair with 27 seconds left for an 88-85 Bulls lead.
Randy Foye's layup pulled Utah to 88-87 with 22 seconds to go, but Chicago sealed it at the foul line.
The win came almost two years to the day that the Bulls beat Utah by six in the finale for Hall of Fame Jazz coach Jerry Sloan, who abruptly resigned the next day.
Sloan was in the arena Friday.
The Jazz held the Bulls to 11 points in the third quarter after giving up 58 in the first half. Jefferson shot 4 of 4 in the period to send the game into the fourth tied at 69.
Jefferson kept it up, too, scoring the first eight Jazz points in the fourth. He couldn't finish off the Bulls, but he was 15 of 22 from the field with 13 rebounds and two blocks.
Utah had a chance late.
Paul Millsap's step-back 3-pointer with 16.9 seconds left missed with Utah trailing 90-87. Luol Deng went 3 of 4 on free throws around a runner by Foye to clinch the victory for Chicago.
Millsap had 21 points for Utah, which had won four of five.
The Bulls led 58-50 going into halftime after shooting nearly 60 percent (24 of 41).
The big difference in the first half was the play of Taj Gibson (5 of 6) and Marco Belinelli (3 of 4), who combined for 17 points off the bench before the break.
Early on, Utah's frontcourt duo of Jefferson and Millsap dominated, scoring 11 points each in the first quarter.
Jefferson opened 4 of 5, spinning by Joakim Noah for a layup, dunking on him and then converting a three-point play to give Utah a 21-16 lead.
Millsap, meanwhile, went right at his former teammate, Boozer, forcing him into two early fouls.
But the Jazz duo didn't get much scoring help.
Utah next plays at Sacramento Saturday night.