Bryant connected on a turnaround jumper from the left side with 2:29 to play to give the defending NBA champions a 99-97 lead and then hit two free throws with 18 seconds remaining to push the lead to three.
The Thunder had two chances to tie it late, but Thabo Sefolosha and Russell Westbrook each missed 3-pointers surrounding a pair of missed free throws by Lamar Odom.
Bryant grabbed the ball after Westbrook's miss and tossed it toward the opposite end of the court to allow the final seconds to run off the clock.
Bryant had been fighting through flu-like symptoms earlier in the day but his fever went down before the game started. He ended up making 9 of 22 shots and turning the ball over seven times, but came through when it counted.
Kevin Durant led Oklahoma City with 28 points but air-balled a pair of shots that could have given the Thunder the lead in the closing minute of regulation and overtime.
He dribbled the ball to run down the final few seconds of the fourth quarter before coming up empty on a deep 3-pointer from the right wing with 2.7 seconds left, but Sefolosha stole the Lakers' ensuing inbounds pass to send the game to overtime.
Durant then air-balled a 17-foot jumper from the right side in the final 30 seconds of overtime that could have put Oklahoma City ahead again. Bryant was fouled intentionally and hit two free throws to provide the final margin.
Andrew Bynum added 22 points, Ron Artest scored 20 and Odom had 13 points and eight rebounds while starting again in place of the injured Pau Gasol.
Jeff Green had 18 points for Oklahoma City while Westbrook and Sefolosha each scored 12.
The Lakers have won their last 10 games against the Thunder franchise, dating back to its days in Seattle.
Sefolosha hit a 3-pointer and a driving finger roll to eliminate a five-point deficit for the Thunder in the final 3 minutes of regulation and tie the game at 88.
Bryant answered at the other end with a turnaround jumper over Sefolosha, but the Thunder got a chance to tie the game after Etan Thomas — playing instead of starting center Nenad Krstic — swatted Odom's floater with one minute to play.
Jeff Green's 12-foot jumper from the left wing tied it with 49.9 seconds left, and Bryant couldn't connect on a desperation 3-pointer at the shot clock buzzer to give Los Angeles a lead. Sefolosha tipped the ball away from Bryant, and he had to scramble to regain possession before shooting.
Durant then aired out the first of his two potential game-winners.
Los Angeles opened the game on a 9-0 run, punctuated by Bynum's two-handed jam off an alley-oop lob from Bryant. The lead reached 28-15 after Bryant finished a spurt of six straight points with a 3-pointer from the right wing over Durant.
But Durant scored 10 straight points, including a two-handed dunk of his own, in a stretch spanning the first quarter break to get the Thunder back in the game.
His two free throws put Oklahoma City ahead for the first time at 41-40, and teams traded 8-0 runs just before halftime to set up a closely-contested third quarter in which the teams traded the lead 13 times.
Notes
Lakers coach Phil Jackson said Gasol had a "pretty good workout" before the game but the team still had no additional information to suggest he has a tear in his right hamstring. The team has described the injury as a strain. … Jackson was asked before the game if he had a fondness for Oklahoma's wide open spaces since he formerly lived in North Dakota, near the Montana border. "Not really fond. There's some sunsets and sunrises that are pretty nice. The wind is aggravating if you live out here, there's no doubt about it." However, he said he remembered listening to Oklahoma City-based KOMA-AM. "There were two radio channels. That was all you could get up there in North Dakota."