In a nip-and-tuck encounter, the Spurs trailed for much of the fourth quarter, but they snatched the lead for good with 2:13 remaining on Tony Parker's lay-up.
Tim Duncan, one of six Spurs players to reach double figures, had 21 points for the Spurs, who again prevailed with a balanced offence.
The Spurs have now won 18 straight games stretching back to the regular season and are the only team to have won every game so far in the play-offs.
Next up is a likely final with the Oklahoma City Thunder, who lead the Los Angeles Lakers 3-1.
LeBron James poured in 40 points and was an assist shy of a triple-double as the Miami Heat beat the Indiana Pacers 101-93 to square their Eastern Conference semi-final series 2-2.
James added 18 rebounds and nine assists to his points haul, while Dwayne Wade contributed 30 points meaning the Heat's two star names accounted for 70 between them in Indianapolis.
The teams will go again in Miami tomorrow [Tuesday].