Paul's late jumper put the Clippers ahead by three points and helped turn back a Spurs rally as Los Angeles improved to 8-3 overall and 3-0 away from home.
The Clippers point guard also dished off eight assists while Blake Griffin helped out with 16 points and 12 rebounds in the victory.
Matt Barnes contributed 14 points, nine rebounds and three steals for Los Angeles.
Tim Duncan netted 20 points and grabbed 14 boards for San Antonio, which fell to 8-3 on the season.
Manu Ginobili supplied 15 points, five rebounds and five helpers in the loss.
2014: The Year in Music [PHOTOS]