Leonard's clutch basket came after Dion Waiters' jump shot with 9.5 seconds remaining put Cleveland ahead 95-93.
The Spurs, who have won 14 of 15, had stars Tim Duncan, Tony Parker and Manu Ginobili on the floor together for the first time since Jan. 13.
Kyrie Irving, who was held to a season-low six points, missed a desperation runner from the top of the key as time expired.
Tony Parker led the Spurs with 24 points while Gary Neal scored 15.
Waiters scored 20 points to lead Cleveland, which has dropped three straight after winning a season-high three in a row.
San Antonio called timeout after Waiters' shot put Cleveland ahead. The Cavaliers had a foul to give and grabbed Duncan with 8.8 seconds remaining. The ensuing inbounds pass went to Parker, who missed San Antonio's win in Chicago with a sore ankle. The Spurs' All-Star guard drove into the lane and found a wide-open Leonard in the right corner. Leonard drilled the clutch shot, giving the Spurs a two-point lead.
Cleveland called timeout and inbounded the ball to Irving, who drove past the 3-point line. Parker's tight defense forced the Cavaliers' All-Star guard to put up a tough shot, which hit the off the rim and fell off.
Irving, who rolled his left ankle Monday against Minnesota, was 2 of 15 from the field with seven assists.
Tyler Zeller, who was scoreless in 25 minutes Monday, had 16 points, including 12 in the first half, for Cleveland.
Cleveland, playing its sixth straight home game, was coming off its worst loss of the season Monday to Minnesota, a 100-92 loss. The Timberwolves played without several injured players, including All-Star forward Kevin Love, but the Cavaliers turned in a lackluster effort from start to finish.
[to top of second column]
Cleveland looked like a different team against the club with the best record in the NBA in the final game before the All-Star break for both games. The Cavaliers built a 10-point lead in the second quarter and was ahead 54-46 at halftime. San Antonio led briefly twice in the third quarter.
Duncan, who had missed eight of the last nine games with a sore left knee, scored 13 points in 25 minutes. Parker, who didn't play Monday because of swelling in his right knee, was 8 of 14 from the field, and had seven assists in 34 minutes. Ginobili, who had missed nine of the last 13 games with a tight left hamstring, had five points in nine minutes off the bench.
Leonard sustained a cut above his right eye in the third quarter and left briefly. He returned wearing a bandage above the eye, scoring 13 points with 10 rebounds.
The Cavaliers used an 11-0 run in the second quarter to take a 37-30 lead. Cleveland led by eight at halftime after Danny Green hit two foul shots throws with 1.1 seconds remaining
-- the Spurs' only made free throws of the half.
Spurs swingman Stephen Jackson missed his second straight game because of personal reasons.
NOTES: San Antonio C Tiago Splitter started after twisting his ankle against Chicago on Monday. ... The Spurs are 4-1 on their annual nine-game, 19-day rodeo road trip. ... San Antonio visits Sacramento on Tuesday. ... The Cavaliers are 3-3 on their seven-game homestand. ... Cleveland is 9-16 this season at Quicken Loans Arena. ... The Cavaliers host New Orleans on Wednesday.
Copyright 2013 The Associated
Press. All rights reserved. This material may not be published,
broadcast, rewritten or redistributed.