Russell Westbrook and Enes Kanter each scored 16 points for Oklahoma City, with Westbrook dishing out seven assists and Kanter grabbing 10 rebounds.
The Thunder, who occupy the eight seed in the Western Conference, had their four-game winning streak stopped.
Oklahoma City hung around early in the first half, but San Antonio turned it up in the second quarter to take a substantial lead at halftime.
There were five lead changes and three ties over the first 12 minutes of action. A pair of Manu Ginobili free throws gave the Spurs an eight-point edge late, then Westbrook scored final eight Thunder points to help them close within 32-28 entering the second.
The Spurs began to distance themselves midway through the second as Marco Belinelli canned a 3-pointer that kicked off a 10-0 run for a 51-37 lead. Leonard's 3-pointer at the buzzer sent San Antonio into the break with a 71-50 advantage.
Diaw's 3-pointer with 5 1/2 minutes left in the third extended the lead to 30 and the Spurs led 100-74 after three quarters.
San Antonio shot 58 percent from the floor ... The Spurs held a 50-36 edge on the glass ... Patty Mills had 11 points and Danny Green and Jeff Ayres each added 10 in the win ... OKC was outscored 56-40 in the paint.