LaMarcus Aldridge clinched the Spurs come-from-behind victory with an offensive rebound and two free throws with 17 seconds remaining.
“It was a great win for us against the really active team,” Spurs coach Gregg Popovich said.
The Spurs, who trailed by 14 points in the first half, improved to 13-3 on the season in front of a crowd of 18,600 Friday at the Boston Garden arena.
San Antonio rallied for their eighth straight NBA win, their ninth in as many games on the road this season, and also beat Boston for the 10th straight time.
Leonard, who finished with 25 points, 10 rebounds and four assists, scored nine points in the fourth quarter.