Nowitzki broke the franchise record of 24 points in any quarter set by Mark Aguirre against Denver on March 24, 1984.
Dallas was down 72-56 after Utah's Wes Matthews hit a layup with 9:51 left. The Mavericks then trailed by 13 before Nowitzki's three-point play triggered a 19-6 run capped by his layup with 2:41 remaining to tie it at 83.
Nowitzki's inside basket on Dallas' next possession put the Mavericks in front for good, 85-83 with 2:05 left. Carlos Boozer's basket with 3:49 to play had given the Jazz an 83-78 edge, but Utah wouldn't score again until Boozer's hoop with 35 seconds remaining.
Nowitzki left to a standing ovation with 28 seconds remaining.
Deron Williams scored 22 points and Mehmet Okur added 14 points and 14 rebounds for Utah.
Jason Kidd had 19 points for the Mavericks (3-1).
Nowitzki went 12-for-22 from the field, 15-for-16 from the foul line, and added 11 rebounds and five blocked shots.
Dallas was able to follow up on victories over the Lakers and Clippers in a two-game weekend trip to Los Angeles with its first home win.
Williams had 12 third-quarter points as the Jazz ended the quarter with a 22-6 spurt for a 67-52 lead.
Utah was up 37-35 after a tough first half for both offenses. The Jazz shot 34 percent from the field and the Mavericks hit 32 percent in the opening 24 minutes.
NOTES: F Drew Gooden (right rib cage muscle) is out for Dallas. ... Mavericks owner Mark Cuban had no comment on claims that Gooden made insensitive comments to a Clippers fan after Saturday night's game. The fan, actor and comic Chris Wylde, was heckling the Mavericks bench throughout the game. ... Cuban also declined to comment on developmental coach Popeye Jones' DWI charge on Sunday night in a Dallas suburb. Jones was not in the arena for Tuesday night's game. ... F Kyle Korver (left knee) and G C.J. Miles (left thumb) are out for Utah. ... Nowitzki has 20 or more points in 29 straight games.