After trailing by 12 in the first half, Los Angeles blew most of an 11-point lead in the fourth quarter. Baskets by Russell Westbrook and James Harden twice cut the Lakers' lead to one in the final 25 seconds, but Bryant and Fisher sealed Los Angeles' 12th straight win over Oklahoma City.
Kevin Durant scored 30 points before fouling out with 1:31 to play, and former UCLA star Westbrook had 21 points and 13 assists for the Thunder, who dropped back below .500 with their fifth loss in six games. Despite a strong start and finish at Staples Center, the Thunder haven't beaten the Lakers since they were the Seattle SuperSonics.
Thabo Sefolosha scored 16 points for the Thunder, but just three after halftime - and the guard missed an open 3-point attempt to tie it in the final two minutes.
Fisher's season high-tying 15 points included two free throws with 14.9 seconds left, followed by a missed 3-point attempt by Westbrook.
Playing at home for the first time since breaking his right index finger in a game against Minnesota, Bryant had another injury scare when he landed awkwardly on his left knee while putting up a backward layup with 5:08 to play. Bryant stayed down on the court for several moments, but shot his own free throws after a timeout - only to take an elbow to the jaw from Westbrook with 3:55 left.
Bryant persevered, drawing Durant's sixth foul before hitting two free throws with 19.5 seconds left in the 102nd 40-point game of his career.
The Lakers returned home after winning the last four games of their first big road trip in a season that began with 17 of their first 21 games at Staples Center. Los Angeles has five more home games in the next two weeks, including a Christmas meeting with Cleveland and a New Year's Day visit from Sacramento.
The Lakers very much resembled a team returning from a long trip in the first half, falling behind by double digits early in the second quarter with poor shooting and indifferent play by Ron Artest, who missed a rebound layup attempt when he inexplicably shot it flat-footed.
Durant and Westbrook led the Thunder to a 61-54 halftime lead. Bryant scored 18 points in the first half, but his fellow starters managed just eight field goals - including none for Andrew Bynum, who went 0 for 5.
Los Angeles made a 13-4 run to open the third quarter, taking the lead on Fisher's 3-pointer.
NOTES: The Lakers have won seven straight home games against Oklahoma City, and 11 straight home games overall. ... Westbrook got a technical foul in the third quarter for throwing the ball at the basket standard in frustration. ... Courtside fans included actors Leonardo DiCaprio and Tobey Maguire, designer Diane Von Furstenburg and husband Barry Diller, and figure skater Michelle Kwan.