The 38-year-old scored 27 points for San Antonio as they dominated the Thunder, who struggled in key defensive areas without the influential Serge Ibaka.
Spurs benefited from a good start as they repeatedly caused problems with experienced duo Tony Parker and Duncan taking the hosts to an eight-point lead at half time.
There were signs of improvement from Oklahoma in the second half, with Russell Westbrook and Kevin Durant beginning to have more of an impact on the game as they contributed 25 and 28 points respectively.
However, a lack of support from their fellow starters, and some key displays off the bench for Spurs, allowed them to pull away in the final quarter.
Parker dealt with a hamstring injury impressively to finish with 14 points and 12 assists in just 36 minutes as San Antonio deservedly took a 1-0 lead over their rivals.