Dallas shot 56 percent from the field and had six players score in double figures. Monta Ellis scored 16 points and reserve Vince Carter added 13.
Derrick Favors scored 19 points for the Jazz, who lost for the 18th time in their last 21 games. Reserve Enes Kanter added 15 points and 19 rebounds, and Richard Jefferson had 15 points.
The Mavericks (48-31) were outrebounded 47-36, but still managed to complete the series sweep of Utah. The Jazz also enjoyed a 52-34 advantage in points in the paint and a 22-7 edge in second-chance points.
Dallas overcame the disparity inside with a terrific shooting performance, including a 9-for-23 night from 3-point range.
The Jazz matched the Mavericks' scoring pace early on. Utah made six straight shots to open the first quarter. Favors had three of those baskets, helping his team to an early 13-6 lead.
Dallas opened the game by making 17 of 18 shots. The Mavericks shot 94.1 percent (16 of 17) from the floor in the first quarter alone. It helped Dallas grab control before the quarter was done.
Samuel Dalembert made back-to-back baskets to tie the game and the Mavericks claimed a 20-18 lead on a Shawn Marion layup with 5:01 left. Dallas eventually made 16 straight baskets before finally missing a second shot.
Wayne Ellington capped that string of 16 consecutive field goals with a jumper on first possession of the second quarter, giving the Mavericks a 41-26 lead.
The Mavs never really cooled down before halftime. Dallas shot 70.3 percent (26 of 37) from the field in the first half, preventing the Jazz from mounting any sort of big rally.
Utah closed to 52-40 after Kanter made back-to-back baskets. Marion then scored on an alley-oop jam to stop the run. He and Ellis each scored a pair of baskets to boost the Dallas lead to 61-44 in the final minute before halftime.
The Jazz made one more attempt to climb back into the game early in the third quarter. Utah trimmed Dallas' lead to 61-51 when Favors made a layup and Gordon Hayward drained a 3-pointer on back-to-back possessions.
Dallas responded by scoring on four straight possessions - culminating with a three-point play by Nowitzki - to take a 70-55 lead.
The Jazz next host Portland Friday night.