Burke went 5-of-10 from beyond the arc for the Jazz, who have won 13 in a row against Milwaukee in Salt Lake City. Derrick Favors added 16 points, 12 rebounds, three steals and three blocks.
Khris Middleton ended with 18 points and six rebounds for the Bucks, who have lost four of five. Michael Carter-Williams contributed 16 points and four steals.
Trailing 54-51, the Jazz ended the third quarter on a 7-1 spurt. Burke scored five of those points to give Utah a 58-55 edge.
John Henson made two free throws to start the fourth, but the Jazz scored the next seven points to build a 65-57 margin. Middleton and O.J. Mayo made consecutive 3-pointers to get Milwaukee within 65-63.
Utah responded with a 9-2 run that Burke capped with a 3-pointer for a 74-65 lead, but the Bucks hung around and cut the gap to 78-75 on layups from Carter-Williams and Giannis Antetokounmpo.
Favors came down with an offensive rebound before making a layup, then blocked Carter-Williams' shot at the other end. The Bucks got the ball back after Trevor Booker's turnover, but Mayo missed a 3-pointer. Gordon Hayward made two free throws with nine seconds left to secure the victory.
The Jazz led by as many as 14 in the first half and took a 47-40 lead into the locker room. But the Bucks started the second half on a 14-4 run to make it a game.
The Bucks haven't beaten the Jazz on the road since Oct. 30, 2001 ... Hayward ended with 14 points for Utah, which went 18-of-23 from the foul line ... Mayo had eight points in his return from a two-game absence due to a hamstring injury ... Each team turned the ball over 23 times.