Spaniard Serge Ibaka contributed 16 points and 11 rebounds while Reggie Jackson added 13 points and six assists in Oklahoma City’s fourth win in five games.
Thunder star guard Russell Westbrook did not play in order to rest his right knee just one month after returning from surgery that had sidelined him for almost two months.
Dion Waiters scored 30 points to lead Cleveland, which lost for the third game in a row and seventh time in nine starts. Spencer Hawes added 20 points for Cleveland.
The Thunder improved to 50-18, matching Indiana for the second-best record in the NBA behind San Antonio.
The Cavaliers, who trailed by as many as 21 in the fourth quarter, made a 16-2 run to pull within 97-92 with 72 seconds remaining.
But Durant sank four late free throws to seal Cleveland’s fate.
At 26-43, the Cavaliers are 6.5 games behind Atlanta for the last Eastern Conference playoff spot.
Oklahoma City connected on 38-of-89 shots from the floor and outrebounded the Cavaliers 53-36, although they surrendered 24 points off 18 turnovers.