The Spurs (19-6) surged ahead in the final quarter courtesy of Tony Parker's 22 points and Gary Neal's 20, to close in on the Thunder's Western Conference-leading 19-4 record.
Kevin Garnett, Courtney Lee, Jeff Green also put up double figures on the scoreboard in a solid team effort.
"We were able to just keep the tempo going," Neal said.
"I think our legs were a little fresher and we were able to keep the tempo pushing forward and knock down some shots."
Starting forward Paul Pierce and bench player Jason Terry contributed 18 points each for the Celtics, but they fell short of claiming a sixth successive victory in San Antonio.
The Celtics have been the only visiting team to do well in San Antonio against a Spurs team boasting an impressive 72-12 record in the regular season at the AT&T Center since the start of the 2010-11 campaign, including a 8-2 mark this season.
"The home court advantage played big for us today, especially with Boston coming off a game last night," Neal added.
"It's always an advantage to play at home. When you make your shots the crowd gets involved and you get your adrenaline going.
"For the most part we fed off the way we all played. When you make the shots the energy just builds on its own and that's what happened today."
The victory came despite Spurs' guard Manu Ginobli leaving the game in the first quarter with heavy bruising on his thigh.