The Thunder, who lost in five games to the Mavericks in last year's Western Conference finals, took a 3-0 lead in the opening-round playoff series.
The defending champion Mavericks will become the first team eliminated from this year's playoffs if they lose Game 4 at home Saturday.
Oklahoma City built a 15-point lead in the first period only to have Dallas rally to within four early in the second. The Thunder then assumed control by halftime and turned the game into a rout by the end of the third period.
Durant made 11-of-15 shots from the field and hit four 3-pointers while playing 40 minutes. Despite being the center of the Oklahoma City offense, he suffered just one turnover.
Russell Westbrook added 20 points for the Thunder and Serge Ibaka had 11 rebounds to go with 10 points.
Dirk Nowitzki, last season's playoff MVP, scored 17 points for Dallas while making only 6-of-15 from the field. The Mavericks shot 34 percent as a team.