Bryant endured a 9-for-25 shooting night to score 36 points, including eight of his team's final 10 points, helping the Lakers get the home win needed in the second-round West matchup.
Kevin Durant tallied 31 points, but missed a long, potential game-tying three-pointer in the final seconds, while Russell Westbrook and James Harden each had 21 in the loss.
The Lakers have less than 24 hours before they will be tested in Game Four back in Los Angeles Saturday. Bryant was asked how much energy he and the Lakers have left for Game Four.
"Plenty," he said with a grin.
While neither team shot well from the field, the Lakers converted a remarkable 41 of 42 free throws, the second highest percentage in play-off history (minimum of 30 attempts) to pull through.
Bryant led the way with a perfect 18-for-18 from the stripe in a clutch victory.
"For us to step up to the free throw line and have the concentration and focus we had there to knock them down is huge," said Lakers coach Mike Brown.
LA squandered a seven-point lead in the final two minutes to lose a heart-breaker in Game Two, but this time they clawed back from a five-point deficit in the final three minutes.
A quick 6-0 run gave Los Angeles a 93-92 lead with about a minute to go and they held off Oklahoma City at the free throw line.
Six Lakers players scored in double-figures, including reserve Steve Blake who had 12 and eight rebounds, while big men Andrew Bynum and Pau Gasol each recorded double-doubles.
"We knew they were going to approach this game with a lot of intensity being down 0-2," Durant said. "We put ourselves in position to win, we'll just keep fighting, man. That's all we can do."
In the Eastern Conference, the
Andre Iguodala scored five consecutive points to break a 83-83 tie and Jodie Meeks finished off the visiting Celtics with four free throws in succession as Boston failed to score in the final 98 seconds.
Iguodala and Evan Turner each had 16 points for Philadelphia, who travel to Boston for Game Five on Monday.
Paul Pierce topped the Celtics with 24 points but Kevin Garnett scored only nine.