Paul Millsap added 15 rebounds and 13 points. Al Jefferson also had a double-double with 14 rebounds and 12 points.
The score was tied at 70 before Mo Williams hit back-to-back 3-pointers then scored on a driving layup. Marvin Williams followed with his second 3-pointer, putting Utah up 11 points with 2:57 left in the third. The Jazz led by as many as 20.
Darren Collison scored 17 points for the Mavs, who pulled off an upset win over the Los Angeles Lakers on Tuesday but couldn't match Utah's pace in the second half.
The Jazz held a 44-30 advantage on points in the paint and 61-40 edge in rebounds as Dallas continued to play without 11-time All-Star forward Dirk Nowitzki and 7-0 center Chris Kaman.
Much was made about how Utah had added 3-point shooters in the offseason, but the Jazz started just 1 of 7 from beyond the arc until Mo Williams starting hitting.
Overall, Utah's three new players -- Mo Williams, Marvin Williams and backup shooting guard Randy Foye -- combined for 55 points and all six of Utah's 3-pointers as the Jazz finished 6 of 14 from beyond the arc.
Brandan Wright added 15 points on 7-of-8 shooting for the Mavs (1-1), while O.J. Mayo and Vince Carter had 12 points apiece.
The Mavs had pulled off the road win over the Lakers, but coach Rick Carlisle knew Wednesday would be just as much of a battle, calling Utah a "wrecking crew" in the paint with its four bigs.
He was right, even if Enes Kanter sat out most of the first half after needing three stitches to close a gash in his chin.
Kanter returned in the third quarter and finished with six points and seven rebounds in 14 minutes.
The Mavs started off hot despite not arriving in Salt Lake City until about 3 a.m., hitting their first five shots in building a 15-8 lead.
Utah pulled even at 18 with 3:51 left in the quarter on Marvin Williams' fast-break layup. He had 10 first-quarter points, including his first 3-pointer as a member of the Jazz.
Still, the Mavs would lead 26-25 after one despite being outrebounded 16-8, and outscored 14-8 in the paint.
The Jazz surged ahead 42-35 in the second quarter as Mo Williams settled in, hitting four shots and two free throws in a 4-minute span.
But the Mavs fought back with six 3-pointers, three by Mayo, two by Jae Crowder and one by Collison that started a 24-8 run and gave Dallas a 63-55 edge at the break.
The Mavs shot 59 percent in the second quarter, hitting 13 of 22 overall and 7 of 8 from beyond the arc.
Unlike Tuesday night when the Lakers made 12 of 31 at the free throw line, the Jazz cashed in there, making 31 of 42 overall.
The Jazz also held a 27-12 advantage on the fast-break as Mo Williams, acquired in an offseason trade, used every opportunity to push the ball.
He finished with six assists and two blocked shots.