"We must all hang together, or we will all hang separately," Bryant said with a smile after the Lakers lost 110-101 on Tuesday night despite his 41 points.
Corey Maggette scored 30 points and Elton Brand had 22 points and 15 rebounds as the Clippers beat the Lakers in consecutive meetings for just the third time since moving from San Diego to Los Angeles before the 1984-85 season.
The Clippers won 105-89 on Jan. 26 in a game Bryant missed because of a sprained right ankle.
"It feels really good," Brand said. "Kobe Bryant missed the last game. With their full complement, to beat them makes it a special thing."
The win was just the Clippers' fifth in the last 33 games between the teams. The Lakers have a 78-21 record against the Clippers since they moved to Los Angeles. The teams split their four meetings this season.
Bobby Simmons added 16 points, Chris Kaman scored 12 and Rick Brunson had 10 for the Clippers (27-34), who shot 51.9 percent and committed only five turnovers in winning for just the fourth time in 15 games.
"That's the way I want us to play," Clippers coach Mike Dunleavy said. "This was probably one of our best passing games we've had all year. We ended up with great shots.
The Clippers were credited with assists on 26 of their 40 field goals, with Maggette and Brunson getting seven each.
"We played really well tonight," Maggette said. "If you play the right way, good things will happen."
Bryant shot 12-of-21 from the floor and made all 16 of his foul shots but scored only six points in the fourth quarter.
"The reason we lost the ballgame is we came out very, very flat to start the game, very, very flat to start the second half," he said. "Now we have to go on the road, where I am sure everybody is counting us out, and seemingly do the impossible."
The Lakers lost despite making all 23 of their foul shots.
By losing for the fifth time in seven games, the Lakers (30-29) fell into a ninth-place tie in the Western Conference with Minnesota -- a half-game behind Denver.
Baskets by Quinton Ross and Simmons gave the Clippers an 81-70 lead with 10½ minutes remaining.
But the Lakers battled back into contention with Jones leading the way, and Odom outscored the Clippers 8-1 by himself to draw the Lakers within one point with 4:36 to play.
However, a 3-pointer by Simmons and a basket by Brunson made it 101-95 with 2:25 left.
Brand was fouled by Chris Mihm as the shot clock was expiring with 1:47 to go, and Odom threw the ball the length of the court in protest. Odom drew a technical foul and was ejected by Olandis Poole. Simmons made the technical and Brand added two free throws to give the Clippers a nine-point lead.
"I was playing bad and my team was playing bad," Odom said in explaining his behavior. "I made a mistake. I overreacted. It was a dumb decision. I'm not using my brain out there. I embarrassed myself and my team. I know it looked bad, but I didn't throw it at a fan and I never intended to hurt anybody."
The Lakers play 15 of their final 23 games on the road.
Maggette had 13 points in the third quarter, when the Clippers outscored the Lakers 33-18 for a 77-70 lead. The Clippers overcame a 52-44 halftime deficit by scoring 16 straight points after Bryant made a basket to start the period.
Bryant scored 12 points during a 16-2 run that put the Lakers ahead 44-33. He finished the second quarter with 18 points -- all in the last eight minutes.
The Lakers led by eight points at the half thanks mainly to Bryant's 25 points and a 16-of-16 effort from the foul line. Bryant made 10 of those free throws.
The Clippers scored the game's first seven points and led by seven on four other occasions before the Lakers went on a 10-2 run for a 20-19 lead.
The Lakers led 28-25 entering the second period.
Bryant has scored 118 points in the last three games and 30 or more in five of the last six games. ... The Lakers, who have a 21-12 record in an NBA-high 33 home games, play their next six games on the road starting Thursday night in Dallas. ... The Clippers snapped a nine-game road losing streak. They hadn't won a road game since beating Memphis 106-103 on Feb. 3. They're 7-22 on the road this season. ... Bryant got hit with a technical foul with 1.3 seconds left in the third quarter after committing a foul on Maggette, who then made three free throws.