Durant landed a perfect 21 from 21 at the free-throw line, with Russell Westbrook adding 31 points for the visitors as the Thunder (32-8) won their sixth straight to continue their dominance in the league.
The Mavericks (17-24) had the Thunder worried after battling from nine down heading into the final quarter time to force overtime when O.J. Majo nailed a three-pointer with 2.3 seconds left.
But Durant landed nine of the Thunder's 12 points in overtime to grab the victory after Mike James failed with a late three-point attempt.
Vince Carter scored 29 from the bench to lead Dallas, who had their four game win streak snapped.