The champions are still standing tall, needing to deliver just one more blow to advance to the next round of the Western Conference playoffs.
All the Spurs have to do is win Game 6 on Thursday night in San Antonio and they will advance to the second round to meet the Houston Rockets.
San Antonio has won 11 of 14 best-of-seven series when tied 2-2.
The Spurs escaped only after the Clippers' DeAndre Jordan was called for basket interference with 4.9 seconds left on a Blake Griffin runner, leaving San Antonio with a one-point lead.
Danny Green made one of two free throws and Kawhi Leonard (18 points) made two free throws for the final margin.
Tim Duncan had 21 points and 11 rebounds to help the Spurs bounce back from their Game 4 loss at home.
The Spurs were going to be forced to show their poise because the Clippers kept coming even after San Antonio built a seven-point lead in the fourth.
When San Antonio's lead was sliced to 107-105 with 1:31 left, the Spurs called a time out.
Out of the timeout, Green missed a jumper.
But Duncan blocked Griffin down low. After Griffin got the ball back, Boris Diaw stripped the ball away.
Tony Parker was fouled, but he made just one of two free throws for a 108-105 Spurs advantage with 48.5 seconds left.
Then after Griffin missed two free throws with 39.9 seconds left, the Spurs failed to get the rebound.
Matt Barnes was fouled and made two free throws to cut San Antonio's lead to 108-107 with 30.8 seconds left.
But the Spurs stayed strong and never let the Clippers score again.
Leonard is Spurs' new star
At some point, the Spurs have maintained, San Antonio will transition into Leonard's team.
The changeover appears to have taken shape in the playoffs.
For the most part, Leonard has carried the Spurs, showcasing his immense skills as one of the NBA's top two-way players.
He has given the Clippers fits in the first four games, dropping a career playoff high 32 points in Game 3.
Before Game 5 Tuesday night, Leonard was leading the Spurs in scoring in the playoffs, averaging 24.8 points per game, eighth-best among players in the postseason.
He was shooting 60% from the field, 56.3% from three-point range.
Leonard has been given more offensive responsibilities in playoffs, doing his best to strike a balance between taking over the game and moving the ball in San Antonio's pace offense.
"Obviously, he's doing a good job," Spurs Coach Gregg Popovich said.
"A player as talented as him, he's certainly someone that we want to see get his touches and that sort of thing. But if he's got an opportunity to score, we want him to do it."
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