The top-seeded Spurs surpassed the 2001 Los Angeles Lakers' 19-game winning streak from the regular season into the play-offs, taking a 2-0 lead in the best-of-seven series on the back of four-game sweeps of the Jazz and the Clippers.
The 1971-72 Lakers hold the longest winning streak of 33 games in the regular season.
Tony Parker exploded for 34 points and eight assists, sixth man Manu Ginobili netted 20 to follow up his 26-point effort in the series opener, and San Antonio treated their fans to yet another triumph since their last loss on April 11.
However, the Spurs seemed less than satisfied with their latest success and coach Gregg Popovich could be seen yelling at Parker in the third quarter even with his team up 16.
"He's been yelling at me for 11 years," Parker said after making 16 of his 21 shots. "We were playing sloppy and OKC (the Thunder) came back on us. He wanted to make sure I kept pushing the ball."
Kevin Durant scored 31 points and James Harden put up 30 for the Thunder, who squandered a nine-point lead in the fourth quarter of Game One but were behind all night in Game Two.
The visitors trailed by as much as 22 points in the third quarter before trimming the deficit to six in the fourth, only for the veteran Spurs to deliver the knockout punch.
Ginobili drained a clinching three-pointer with 1:29 left to establish a 10-point advantage, letting out an intense scream to signal the triumph.
"We fought hard but it was too big of a deficit," Harden said. "We can't put ourselves in that situation."
Having lost only one game from the first two rounds of the play-offs, the Thunder will hope to claw back into the series in Game Three on Thursday when they head home to Oklahoma City.