Parker was 16-of-21 from the field but just 1-of-2 from the free-throw line. He went 1-for-2 from 3-point range.
Manu Ginobili added 20 points for the Spurs. Kawhi Leonard scored 18 plus 10 rebounds, and Tim Duncan also had 11 points and 12 rebounds.
Kevin Durant led Oklahoma City with 31 points and James Harden had 30 off the bench. The Thunder shot 42 percent from the field but was 8-for-17 from 3-point range.
The Thunder trailed by as much as 22 points and were outscored in each quarter except the fourth when they outscored the Spurs 35-28 and whittled the deficit to 93-99 with 5:40 to play in the game.
Game 3 is set for Thursday in Oklahoma City.
Celebrity Families of 2014 [PHOTOS]