The Thunder had erased a 13-point deficit with less than 11 minutes left to forge a 111-111 tie when Durant fired in a 3-pointer over the Timberwolves' Dante Cunningham for the game-winner.
The T-Wolves had a chance to regain the lead when Kevin Love was fouled attempting a 3-pointer at the other end. But he missed the first two foul shots and couldn't find the rim when he intentionally missed the third.
Durant scored 23 of his points in the fourth quarter as Oklahoma City notched an eighth straight road win.
Love provided 30 points with 14 rebounds and Nikola Pekovic added 31 and 11 for Minnesota.
Kevin Martin put in 17 points.
Notable deaths of 2014 [PHOTOS]