Ryan Anderson's 3-pointer with 15 seconds left pulled the Hornets within 100-97 but Randy Foye and Millsap each hit two free throws down the stretch to seal it.
Coming off a 45-point loss to Houston on Monday, the team's worst home loss ever, the Jazz trailed by 12 points in the first quarter before rallying to take a 10-point lead with about 7 minutes remaining.
Anthony Davis nearly brought the Hornets all the way back with an eight-point fourth quarter. He pulled them to 95-94 with 2:18 remaining but Millsap and Jefferson hit back-to-back shots that provided the cushion Utah would need.
Greivis Vasquez led the Hornets with 17 points and 13 assists, but made just 8 of 21 shots after starting 4 for 5.
Millsap added 10 rebounds and two blocks.
Early on, the Jazz resembled the team that was embarrassed by the Rockets in their worst home loss in franchise history.
They trailed by 12 and couldn't hit a shot or defend one, shooting under 30 percent at one point while the Hornets opened 7 of 10.
Anderson and Roger Mason, starting in place of Eric Gordon, each hit two 3s as the Hornets looked strong despite coming off a loss to the Los Angeles Lakers on Tuesday night.
The Jazz climbed back into the game in the second quarter behind Derrick Favors and Earl Watson.
Watson pushed the pace and Favors was a beast inside, hitting 4 of 4 shots in the quarter and corralling three rebounds.
Utah also dominated the paint in the second, holding an 18-8 edge on points.
DeMarre Carroll's fast-break layup tied it at 39 with 5:59 left in the half and Utah took a 51-47 lead into the break, with Millsap finally scoring a field goal after starting 0 for 4.
Millsap got going in the third, scoring 11 points as the Jazz took a 78-75 lead into the fourth.
Utah quickly bumped it to eight, Burks hitting a 3-pointer on a nice feed from Millsap. The Jazz increased the lead to 90-80 on a pair of free throws by Burks with 7:16 remaining.
Davis then made it a game, finishing with 14 points as five Hornets players scored in double figures
Utah also had five players in double figures, with Favors adding 15 points, Foye 14 and Marvin Williams 11.
After shooting just 38.1 percent in the first quarter, the Jazz finished at 50.
Both teams were missing key players, with the Jazz still without starting point guard Mo Williams (thumb surgery) and third-leading scorer Gordon Hayward (sprained shoulder.)
The Hornets held out leading scorer Gordon, held out as part of medical protocol on the second game of back-to-backs.