Tim Duncan got banged up early on, leaving the game in the first quarter to get his right knee examined before returning to the court to post 20 points and 15 boards for the Spurs, who had lost two of three following 19 consecutive wins. Danny Green hit five 3-pointers for 15 points, and Tiago Splitter netted 12 points. The Spurs moved to 24-0 on the season when Splitter scores in double figures.
San Antonio needs to win just one of its final three games or have Oklahoma City lose once to clinch the Western Conference's No. 1 seed.
Dallas, meanwhile, fell into a virtual tie with Phoenix for seventh place in the Western Conference with the loss. The Mavs have played two more games than the Suns, and the two teams are set to do battle in Dallas on Saturday.
The Spurs won their eighth straight game against Dallas, completing a second straight season sweep for the first time since earning three straight from 1991-94.
Green started a perfect 3-of-3 from behind the arc, and the Spurs rode his hot hand to a 15-5 start.
Dallas trailed 30-22 after one but got a pair of quick jumpers from Nowitzki, forced two Manu Ginobili turnovers and tied the game on Brandan Wright's alley-oop slam on a touch pass from Jae Crowder. The Mavericks used a prolonged 16-2 run against San Antonio's reserves to open the frame and go in front, 38-32.
San Antonio didn't blink, however, running off 11 straight to jump back in front.
Nowitzki's free throws with 17 seconds left in the half gave the Mavs a 51-49 lead at the break.
The second half belonged to the Spurs. Mills' 3-pointer at 8:26 of the third capped a 14-4 flurry. Leonard then grabbed a pair of offensive boards in traffic after Mills missed a semi-contested fastbreak layup and fed Mills on the left wing for another 3-pointer and a 66-58 lead.
Dallas never got closer than five the rest of the way and trailed by double digits for much of the fourth.
Devin Harris and Jose Calderon hit triples to bookend an 8-0 charge late in the fourth to pull Dallas within six, but with just under a minute remaining, Leonard countered with a 3-ball from the left corner that sealed the outcome.