LOS ANGELES (AP) -- Just when it appeared the Los Angeles Clippers were doomed, they rallied for a dramatic and much-needed win for their playoff hopes.
Harris made 11 of 19 shots and Williams scored 15 points in the final quarter to spark the Clippers' comeback. It was the 37th time this season Williams has scored 20 or more as a reserve.
''We stayed focused, cut into their lead and found a way to win,'' said Harris, who had his highest-scoring game as a Clipper. ''In the fourth quarter, we were aggressive, got good looks, got stops and got out in transition.''
Austin Rivers scored 18 points and Montrezl Harrell had 16 points for Los Angeles. DeAndre Jordan scored 10 points and grabbed 17 rebounds.
''It was my favorite win of the season,'' Rivers said. ''We had no choice. If we quit on the game, we quit on the season. We had nothing to lose or be discouraged about. They're one of the best defensive teams in the league and to do it against them is big.''
LaMarcus Aldridge scored 35 points for the Spurs. Patty Mills added 17 and Rudy Gay scored 13 points.
San Antonio (45-33) is tied for 4th place in the Western Conference with Utah. The Spurs have four games remaining, two on the road and two at home.
The Clippers are in 10th place, 1 1/2 games behind New Orleans for the eighth and final playoff spot. They have four games remaining, three at home and one on the road.
''It's hard to explain any of our wins,'' Clippers coach Doc Rivers said. ''I just thought we hung in there. The Spurs are such a tough team because of their movement. Every time we cut it to one, they get it back to 10, we cut it to one and they get it back to 10, but it was well-played game at both ends and we made some big shots.''
Williams' basket tied the score at 103 with 1:58 to play and he gave the Clippers a 106-105 lead with a bucket with 50 seconds remaining.
Mills countered with a 3-pointer to give the Spurs a 108-106 lead with 37 seconds left, but Rivers answered by drilling a 3-pointer to give Los Angeles a 109-108 lead.
''I just have that confidence and it's due to my teammates giving me that,'' Austin Rivers added. ''They expect me and Lou and Tobias to shoot those shots down the stretch, so I know I can't afford to get into my own head.''
Williams and Harris combined to hit four free throws in the final seconds to secure the win.
San Antonio had one more shot to tie the game but Manu Ginobili stepped out of bounds as he was attempting a 3-pointer with 2 seconds remaining.
''That's a tough loss,'' Spurs coach Gregg Popovich said. ''We can't give up 42 points in a quarter, especially in the fourth quarter of a basketball game on the road, but we were undisciplined. I think the defense caved in the fourth quarter. It's very disappointing, but our lack of discipline really hurt us, and I thought their aggressiveness, their physicality was great and they did a great job.''
The Clippers trailed by 19 points in the second quarter, but rallied and took a 64-63 with 5:29 remaining in the third quarter, following a three-point play by Jordan.
However, Aldridge scored nine points over the final 4:24 of the third quarter as the Spurs built an 83-72 lead after three periods.
Williams is averaging 22.7 points and leads the NBA with 595 fourth-quarter points this season.
San Antonio fell to 14-25 on the road.
San Antonio led 31-17 after the first period. The Spurs increased their lead to 49-30 but the Clippers countered with a 19-7 run over the final five minutes of the quarter to cut the lead to 56-49 at halftime.
Harris made seven of 12 shots and led the Clippers with 17 points in the first half. Both teams shot over 45 percent in the opening half.
San Antonio: Since joining the NBA in 1976, the Spurs have accumulated the best winning percentage in NBA history (.623) ... Entering Tuesday's game, the Spurs led the league in fewest points scored by their opponents per game (99.2).
Clippers: Harris is averaging career-highs in points per game (18.6) and in 3-point percentage shooting (41.6). ... The Clippers are 40-126 all-time against the Spurs. ... F Danilo Gallinari missed Tuesday's game with a hand injury.
At a press conference held on Monday at the Jim Gilliam Recreation Center in South Los Angeles, Steve and Connie Ballmer, along with the Clippers, announced a multimillion-dollar donation to the L.A. Parks Foundation. The money will go toward renovating nearly 350 basketball courts in city parks by the year 2021.
Spurs: Remain in Los Angeles and play the Lakers on Wednesday.
Clippers: Travel to Salt Lake City to play the Jazz on Thursday.