Houston missed its first seven shots of overtime before Danuel House made a 3-pointer with less than a minute left. By then it was too late.
Game 4 of the best-of-seven series is Monday.
The Thunder had a balanced scoring attack, with Shai Gilgeous-Alexander adding 23 points and Danilo Gallinari had 20. Jeff Green had 22 points for the Rockets. They have played the entire series without Russell Westbrook, who is out with a strained right quadriceps.