Trailing by 24 points early in the second quarter, the Spurs seized control through All-Stars Tony Parker and Tim Duncan to take a commanding 3-0 lead in their best-of-seven Western Conference semi-final series.
Guard Parker recorded 23 points and 10 assists while towering forward Duncan weighed in with 19 points and 13 rebounds as San Antonio extended their unbeaten run to 17 games, including seven in the playoffs.
Blake Griffin, despite playing with a left hip injury and a sprained right knee, led the way for the Clippers with 28 points and 16 rebounds but his heart-broken team paid the penalty for poor free shooting, making only 50 percent from the stripe.
"To start the game, the Clippers played very aggressively and played great defense," Spurs coach Gregg Popovich said. "On top of that, they made their shots, we didn't make ours and we were in transition a lot.
"We called some plays that helped us and Tony (Parker) ran the show really well. He knows what's going on out there and it just worked out for us tonight."
Thirteen-time All-Star forward Duncan applauded his team's composure under the early pressure piled on by the fifth-seeded Clippers.
"We understood that they were going to make a run early and we needed to sustain," he said. "We've been through enough of them (playoff games) to understand that's how it goes.
"It was great poise by our entire team. We were lucky enough in that second half to start making some shots and making some stops."
The fast-paced Clippers made a rousing start in front of a sellout crowd of 19,060, racing into a 27-9 lead after a sizzling 14-0 run sparked by forward Griffin before ending the first quarter 33-11 ahead.
The Staples Center was a vocal sea of red with most of the home fans wearing giveaway red T-shirts emblazoned with the words "Clipper Nation All In".
Los Angeles briefly stretched their lead to 24 points when Nick Young poured in a three-pointer but, with Parker and Duncan beginning to make an impact, the Spurs cut the deficit to 53-43 by halftime.
San Antonio tightened their defense and, as the Clippers struggled to find the basket, the visitors took the lead for the first time at 59-57 after a Duncan fadeaway jump shot capped a stirring 14-0 run.
The Spurs extended that unbroken run to 24-0 before ending the third quarter with a 69-61 advantage.
San Antonio maintained their grip in the fourth quarter, repeatedly fouling Clippers reserve forward Reggie Evans who made just three of 10 free throws as time ebbed away.
Game Four is in Los Angeles on Sunday when the Spurs will look to complete a 4-0 sweep and the Clippers will bid to become the first team ever to win an NBA playoff series after trailing 0-3.
"We have to keep fighting," said Clippers All-Star guard Chris Paul, who contributed 11 assists and just 12 points while still being hampered by a strained right hip. "It's never been done before in history.
"We were desperate in Game Seven in Memphis and you saw how we came out and played," he added, referring to his team's road win over the Grizzlies to clinch their Western Conference quarter-final.
"Hopefully we can be the best for the next four games."