The Knicks won for just the 10th time this season, leaving only Milwaukee with fewer than 10 victories for the campaign. It was the sixth win on the road for New York, two more victories than the Knicks have at home.
Anthony and Shumpert both scored 27 points with Anthony returning from a three-game absence brought on by a knee injury.
The game was tied when Anthony attempted a 3-pointer that bounced high off the rim. Schumpert was there to tap the ball off the glass and through the basket for a 103-101 lead.
Marco Belinelli then missed a 3-point try for the Spurs and Anthony hit two free throws to account for the final score.
Belinelli scored a career-best 32 points, hitting six 3-pointers. San Antonio had won its previous three games.