Stephen Curry bounced back from a slow start to finish with 29 points, 10 rebounds and nine assists.
The Warriors, who set the league's regular-season record with 73 wins, will host Game 7 on Monday. The winner will play Cleveland in the NBA Finals.
Oklahoma City dominated Games 3 and 4 at home, but the Warriors made 21 of 44 3-pointers on Saturday, while Oklahoma City was 3 of 23.
Kevin Durant scored 29 points and Russell Westbrook added 28 for the Thunder. But Durant made just 10 of 31 shots and Westbrook was 10 of 27.
