Tim Duncan had 26 points and 10 rebounds as San Antonio pulled away in the third quarter to win Game 1 of the Western Conference semifinal series.
Manu Ginobili scored 13 of his 22 points in the second half to help the Spurs run their winning streak to 15 games.
Kawhi Leonard and Danny Green added 16 and 15 points, respectively, for San Antonio, which tied a franchise postseason record by burying 13 3-pointers in 25 attempts.
Eric Bledsoe came off the bench to score a team-high 23 points and Blake Griffin and Caron Butler added 15 points apiece for Los Angeles. Clippers All-Star point guard Chris Paul, playing with a strained hip flexor, had six points in the first quarter but was scoreless the rest of the way. He had 10 assists.
San Antonio will host Game 2 on Thursday night.
The Spurs came out on fire in the third quarter, hitting 10 of their first 16 shots to stretch an eight-point halftime lead to as many as 19 points before taking an 87-72 edge into the fourth.
Bledsoe rallied the Clippers early in the fourth, scoring six points in a 10-0 run to cut the deficit to 90-82 with nine minutes remaining.
Los Angeles, which erased a 27-point deficit to win Game 1 at Memphis in the first round, got no closer as the Spurs beat the Clippers for the 18th time in the last 19 meetings in San Antonio.
San Antonio used a 9-0 run to open an eight-point lead late in the second quarter and took a 57-49 lead to the locker room. Duncan had 12 points and Danny Green added 11 to lead the Spurs while Griffin topped the Clippers with 10 points.
GAME NOTEBOOK: Los Angeles C DeAndre Jordan had seven points and eight rebounds in the first quarter - matching his highs for the postseason - but sat out the entire second quarter after picking up two fouls. ... The Spurs had won 17 straight home games against Los Angeles until a 120-108 defeat on March 9. PG Tony Parker sat out the loss. The Clippers' previous victory in San Antonio came on Jan. 31, 2002. ... Paul committed four turnovers in the second and third quarters and finished with five.