Bryant scored 40 points, 10 in the final 5:38, to lead the Lakers to a 105-101 victory on Tuesday night.
"As players, it's just another game. But when the whole city gets involved with this atmosphere, we can't help but respond," Bryant said, alluding to the sellout crowd of 18,997 for what was a Lakers' home game against their neighbors from down the hall.
The 40 points were a season high for Bryant, who's been working his way back from offseason knee surgery.
He got the Lakers going again after they went scoreless over a span of almost seven minutes beginning in the final minute of the third quarter and extending into the fourth.
"I'm just setting the tone. I'm just coming out and been aggressive and reading the defense in the second half," Bryant said.
Lakers coach Phil Jackson was pleased to see Bryant, the NBA's top scorer last season, hitting his stride.
"The thing I looked at is that he had one turnover tonight," Jackson said. "I think the decisiveness is evident.
"He's doing things a little quicker, making his moves a little quicker, with not as much hesitation."
Bryant went 12-of-23 from the field and 15-of-18 from the line.
"He got to the line and had some points and that's really what carried us because Lamar (Odom) had a nightmare of a game," Jackson said.
Odom finished with 18 points, but was 6-of-18 from the floor, 4-of-10 from the line and committed four turnovers.
Kwame Brown had 10 points and 14 rebounds for the Lakers.
Elton Brand led the Clippers with 20 points and 15 rebounds, and Corey Maggette had 20 points in the first of four meetings this season between the teams that share the same homecourt. Chris Kaman had 12 points and 10 rebounds for the Clippers when he fouled out with 5:15 remaining.
"Laker fans were happy, Clipper fans were sad," Clippers coach Mike Dunleavy said. "We did a great job on Kobe. He got to the free throw line on us and that's probably the difference in the game."
Ahead by 13 late in the third quarter, the Lakers gave up all that lead by going scoreless over the first 6:22 of the fourth.
Bryant ended the scoring drought with a pair of free throws, then finally made the Lakers' first shot from the field with 4:35 left in the game.
Brown's two free throws gave the Lakers the lead again at 92-91. They opened a 98-91 pad on Luke Walton's layup with 1:26 remaining and stayed in the lead.
Bryant made several spectacular shots down the stretch, including a drive when he did a 360-degree spin as he neared the basket, lofted the ball high and watched it drop back through the hoop for a 94-91 lead with 2 1/2 minutes remaining.
The Clippers, down 79-66 with 2:40 left in the third quarter, closed to 83-74 by the end of the period. They drew even at 83 on Shaun Livingston's 3-pointer 3:16 into the fourth, his ninth point in the Clippers' comeback -- and his only points of the game.
Sam Cassell scored 12 of his 18 points in the third quarter to help the Clippers stay close.
After a loud first quarter when he scored 20 points on 7-of-11 shooting, Bryant quieted down, made one of his two shots and had three points in the second quarter. Still, the Lakers led 51-48 at halftime.
The teams have played each other 170 times, 103 of them since the Clippers moved from San Diego to Los Angeles in 1984. The Lakers hold a 127-43 all-time edge. ... Shaquille O'Neal scored 61 points in a Lakers' victory over the Clippers on March 6, 2000, and Lakers coach Jackson said the Clippers started becoming competitive after that. "Now they've got the right combination of people," Jackson said.