Kevin Durant led the Thunder with 32 points and Russell Westbrook added 19, making all eight of his free throws.
Pau Gasol had 25 points and 12 rebounds, and Andrew Bynum had six points and 10 boards for the defending champions, who failed to sustain their strong start for the second straight game.
Game 3 is Thursday in Oklahoma City. The Lakers are 39-1 all-time when winning first two games of a best-of-seven series.
The Thunder's defense kept them in the game, with 17 blocked shots.
Bryant scored 15 points in the fourth, but sent the crowd into an anguished groan when he missed the first of two free throws with 15 seconds left. He made the second to keep Los Angeles ahead 94-92.
Durant missed a 3-pointer and Gasol got fouled, but he also missed the first with 7 seconds left, keeping the Thunder's hopes alive. Gasol hit the second, and then Jeff Green, who had 12 points, missed a 3-pointer as time expired.
The Thunder led three times, but Bryant twice brought the Lakers back, the last time tying the game at 88 on two free throws. The game was decided at the line over the final 2:20, with the Thunder forced to foul while missing from the perimeter.
The Lakers regained the edge in the third quarter, although not by much. Their largest lead was six and it dwindled to 73-69 going into the final 12 minutes. Durant was called for goaltending on the Lakers' last basket or the Thunder would've trailed by two.
With every starter except Bynum on the bench to start the second quarter, the Lakers extended their lead to 37-26. But the Thunder outscored them 21-8 to lead 47-45 going into halftime, despite Westbrook picking up his third foul midway through the period.
Durant had nine points in the spurt, with he and Green hitting back-to-back 3-pointers. The Lakers were limited to 33 percent shooting, with Bryant going 2 of 7. The Thunder had nine blocked shots in the half.
Bryant's jumper hit the rim and went in to tie the game at 45 before Eric Maynor beat the shot clock on a fadeaway jumper, giving Oklahoma City its first halftime lead of the series.
The Lakers owned the first quarter in a repeat of their strong start to Game 1. They outscored the Thunder 26-18, with Bryant scoring eight of their first 13 points. The Thunder shot 29 percent from the floor.
NOTES: The Lakers unveiled a bronze statue of late announcer Chick Hearn outside Staples Center before the game. ... Craig Calloway of Compton hit a halfcourt shot between the third and fourth quarters and won $235,000. Phil Jackson saw it, interrupted his TV interview, smiled and said, "Somebody made a shot. It wasn't us." ... Celeb sightings: Charlize Theron, David Beckham, Kid Rock, Jack Nicholson, David Spade, Adam Levine, Andy Garcia, Minnesota Timberwolves coach Kurt Rambis, and Hall of Famer Elgin Baylor.