Seven points clear with two minutes left, the Spurs struggled to close out the game and could have fallen behind with five seconds left when DeAndre Jordan tipped in Blake Griffin’s shot – but the score was disallowed for basket interference and free throws from Danny Green and Kawhi Leonard made the game safe.
Veteran Tim Duncan led the way with 21 points and 14 rebounds and Leonard added 18 points, giving the Spurs the chance to wrap up the series in game six on Thursday.
Griffin led the Clippers with 30 points and 14 rebounds.
The Houston Rockets secured their place in the next round after a 103-94 victory over the Dallas Mavericks.
James Harden was the star with 28 points, while Terrence Jones added 10 in the fourth quarter as the Rockets completed a 4-1 series win and their first play-off triumph since 2009.
The Rockets were a different side to that which lost 121-109 in game four, with Dwight Howard adding 18 points and 19 rebounds while Josh Smith scored 20 points.
Monta Ellis led Dallas with 25 points and Dirk Nowitzki added 22 but it will be the Rockets who will face the winners of the Clippers-Spurs series.