Kevin Durant led the Thunder with 36 points and 8 rebounds. Russell Westbrook pitched in with 27 points and 11 assists.
LeBron James had 30 points and 9 rebounds for the Heat. Dwyane Wade and Chris Bosh combined to go 11-for-30 from the field, totaling 29 points.
The Heat got significant scoring contributions from Shane Battier and Mario Chalmers, but 23 of their 29 points came in the first half when Miami was in control.
Game 2 is on Thursday at 6 p.m. PT on ABC7.