Bryant's jump shot with 7:54 to play in the first half gave him 31,421 career points, taking him past Wilt Chamberlain's total of 31,419.
Only Kareem Abdul-Jabbar (38,387), Karl Malone (36,928) and Michael Jordan (32,292) stand ahead of Bryant in the all-time list, but Bryant admitted passing the iconic Chamberlain was special.
"He was such a warm-hearted gentleman," he said.
"I have nothing but praise for him. To pass him up is a huge honor to say the least."
The 34-year-old insists he's more concerned with gaining a sixth NBA title as the struggling Lakers battle to reach the playoffs.
Point guard Steve Nash was dealing with a sore hamstring and painful hipm and lasted less than two minutes, but Bryant played 47-plus of 48 minutes, finishing just shy of a triple-double with 19 points, 14 assists and nine rebounds.
"Sometimes you've got to will your way through it. Now is not the time to sit back," said Bryant, who spent just 23 seconds on the sideline despite suffering from a bone spur in his foot.
He said he decided in the first quarter that he wouldn't let coach Mike D'Antoni take him out of the game for his usual minutes of rest.
Dwight Howard led the Lakers with 24 points and 15 rebounds and Pau Gasol was the third Laker with a double-double, adding 12 points and 10 assists.
The victory kept them neck-and-neck with the Utah Jazz for the eighth and final playoff berth in the Western Conference.
Russell Westbrook had a triple-double as he and Kevin Durant combined to lift the Oklahoma City Thunder to a 109-99 win over the Milwaukee Bucks.
Westbrook had 23 points, 13 rebounds and 10 assists, while Durant poured in 30 points.
Ersan Ilyasova led Milwaukee with 29 points and 14 rebounds.
Dirk Nowitzki poured in 35 points, including the game-winning three-pointer, as the Dallas Mavericks claimed a 100-98 win over the Chicago Bulls.
Nowitzki's score with less than three seconds remaining capped a fourth-quarter rally from the Mavericks, who had trailed by 12 points.
Stephen Curry had a big night, scoring 39 points to help the Golden State Warriors ease past the Portland Trail Blazers 125-98.
Carl added 25 points and 10 rebounds for the Warriors, while Meyers Leonard led Portland with 22 points and 10 boards.
Paul George scored 25 points and Roy Hibbert added 20 to lift the Indiana Pacers to a 112-104 victory over the Phoenix Suns.
Randy Foye had 26 points to help the Utah Jazz to a 116-107 win over the Brooklyn Nets and the Memphis Grizzlies overcame the Minnesota Timberwolves 99-86 on the back of 21 points from Marc Gasol.
The Atlanta Hawks saw off the Orlando Magic 97-88, the Houston Rockets beat the Los Angeles Clippers 98-81 and the Philadelphia 76ers were 100-92 winners over the Charlotte Bobcats.
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