Kobe Bryant and Andrew Bynum scored 20 points apiece for the Lakers, who came up empty on their last six possessions after Bynum's hook shot made it 75-68 with 2:09 remaining.
After struggling throughout the second half, the Thunder suddenly came alive after Scott Brooks called timeout following Bynum's basket that gave Los Angeles its largest lead of the game.
James Harden drove for a layup before Durant used his height advantage to reach up and tip away a pass from Bryant, who he was guarding. Durant ran out for a right-handed dunk at the other end before Russell Westbrook forced another turnover by aggressively challenging an outlet pass to Bryant along the sideline.
Harden made the next stop, blocking Bryant's jumper on the next Lakers possession and getting a layup in transition off it to cut the deficit to one in the final minute.
Bryant couldn't connect again, this time on a 3-pointer, to give the Thunder the ball back with the chance to take the lead and Durant was able to make it happen.
Steve Blake missed a 3-pointer from the right side with about 5 seconds left after Metta World Peace couldn't get the ball to Bryant on the inbounds play. Durant was then fouled with 0.3 seconds left and made his first try before missing the second on purpose failing to hit the backboard or rim for a violation.
The Lakers got a desperation try but World Peace's long pass for Bynum was intercepted by Harden.
Westbrook added 15 points for Oklahoma City, which matched its lowest scoring total of the season but still gutted out the win.
Historically, the loss makes a huge difference. Los Angeles is 29-12 when splitting the first two games of a seven-game series and has lost 17 of 19 when falling into a 2-0 hole. The Lakers' last comeback was in the 2004 West semifinals against San Antonio.
The Thunder have won all nine of their series after leading 2-0, dating back to the franchise's days in Seattle.
In a game that was nip-and-tuck throughout, the Lakers started inching away early in the fourth quarter while Westbrook was on the bench.
Bryant drilled a jumper from the left wing and Blake followed with a 3-pointer before World Peace hit one of two free throws for a 69-63 advantage with 7:27 remaining the Lakers' largest lead to that point.
Westbrook returned then but only provided the briefest of sparks for the struggling Oklahoma City offense, and Bynum's second straight basket on a left-handed hook shot at the left block made it 75-68 with 2:09 to play.
Until that point, Oklahoma City had made only 7 of 27 shots in the second half while committing eight turnovers.
After getting ripped apart by the Thunder's pick-and-roll attack and giving up 119 points in Game 1, the Lakers made it an emphasis to put up more resistance in the rematch and it showed. Matt Barnes shuffled back and forth around three Nick Collison screens to contest Harden's jumper and preserve the Lakers' 22-21 lead after one quarter.
The Lakers' defense was at its best just after halftime as they got out of a 48-45 deficit by holding Oklahoma City scoreless for the first 4 minutes and allowing just two baskets in the first 8 minutes. But Los Angeles still couldn't create any sort of a cushion and Westbrook's wide-open 3-pointer from the left corner after World Peace airballed a similar shot on the opposite end had the Thunder back within 57-56 with 3:31 left in the third.
Boston 107, Philadelphia 91
Boston leads series 2-1
Oklahoma City 77, L.A. Lakers 75
Oklahoma City leads series 2-0
Miami at Indiana, 5 p.m., ESPN
Series tied 1-1
L.A. Clippers at San Antonio, 7:30 p.m., ESPN
San Antonio leads series 1-0