Durant drained a go-ahead three-pointer with 41.9 seconds remaining and the Thunder held on to take a stranglehold on the Western Conference first-round series.
No NBA team have come back from an 0-3 deficit to win a best-of-seven post-season set.
Durant carried Oklahoma City in the absence of Russell Westbrook, who had surgery to repair a torn meniscus in his knee on Saturday and will miss the rest of the playoffs.
In Memphis, the Grizzlies mauled the Los Angeles Clippers 104-83 to pull level in their Western Conference series at 2-2. Marc Gasol and Zach Randolph scored 24 points apiece to power the Grizzlies, who will travel to Los Angeles for game five on Tuesday and host game six on Friday.