Leonard's clutch trey gave him 13 points for the game to go with 10 rebounds as the Spurs pulled out a third straight win heading into the NBA All-Star Game break.
Tony Parker contributed 24 points, seven assists and six rebounds in his return from a one-game absence with a sore knee.
Tim Duncan made his first appearance in four games and responded with 13 points and six rebounds for San Antonio, which won for the 14th time in 15 contests overall.
The Cavaliers got 20 points and six rebounds from Dion Waiters but still dropped their third straight.
Swim Week Miami Beach 2014 [PHOTOS]