Durant finished with a game-high 37 points for the Warriors, who beat the Spurs for the third straight time this season and fourth straight time overall.
LaMarcus Aldridge had a team-high 30 points for the Spurs, who were opening a rugged three-game trip on which they also will face Oklahoma City and Houston.
Curry was injured on the Warriors' sixth possession of the game. He stepped on DeJounte Murray's foot after getting fouled on a layup attempt, twisting his troublesome right ankle.
Curry was able to shoot the two free throws, but immediately left the court at the 9:38 mark of the first period and never returned.
Warriors coach Steve Kerr said Curry will not play Friday at Portland on the second night of a back-to-back.
The Spurs led 101-93 before Durant scored the Warriors' next 12 points, including a 3-point basket and three free throws when fouled on another 3-point attempt, during a 12-4 run that drew the Warriors even at 105-105 with 2:02 to play.
Green's hoop happened after he appeared to attempt a lob pass that hit off the backboard and caromed right back to him. He then floated in a six-footer for a lead the Warriors never relinquished.
Green's hoop capped an 11-point, 12-rebound, 10-assist triple-double. His rebound and assist totals were team highs.
Durant, who hit 14 of his 26 shots, added 11 rebounds for Golden State, which remained unbeaten (7-0) since the All-Star break.
Klay Thompson and JaVale McGee chipped in with 13 points apiece for the Warriors, who shot just 8-for-30 on 3-pointers.
Aldridge complemented his 30 points with a game-high 17 rebounds for the Spurs, who had won 110-94 at Cleveland in their most recent road game.
Kyle Anderson had a 12-point, 11-rebound double-double for San Antonio, while Murray had 14 points, Davis Bertans 13, Tony Parker 11 and Rudy Gay 10.
Murray also collected a team-high six assists.
The Spurs connected on just six of their 22 3-point attempts.
--Field Level Media
San Antonio | Golden State | |
LaMarcus Aldridge 30 | Scoring | Kevin Durant 37 |
Tony Parker 7 | Assists | Draymond Green 10 |
LaMarcus Aldridge 17 | Rebounds | Draymond Green 12 |
LaMarcus Aldridge 8 | Free Throws Made | Kevin Durant 5 |
Kyle Anderson 5 | Steals | Draymond Green 3 |
Rudy Gay 1 | Blocks | Kevin Durant 4 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
San Antonio | 107 | 45.3 | 6-22 | 15-18 | 29 | 45 | 3 | 7 | 12 |
Golden State | 110 | 43.2 | 8-30 | 20-23 | 30 | 49 | 12 | 6 | 10 |