Matt Barnes had 15 points and 10 rebounds for the Lakers, who rallied and broke the game open in the fourth quarter to win their fourth straight game. The Lakers trailed by four when Barnes and Odom sparked them during a 27-8 run.
Spencer Hawes had 18 points and 13 rebounds, and Andre Iguodala scored 18 points for the Sixers.
The season's second sellout crowd of 20,366 included some of Philadelphia's top sports stars. Kobe Bryant scored only nine points a night after his high school dedicated the gym in his honor.
Bryant sprained the pinky finger on his right hand in the first quarter but still played 36 minutes. Coach Phil Jackson said Jackson would be fine.
Philadelphia Phillies Jimmy Rollins and Ryan Howard were at the game. So was Eagles wide receiver DeSean Jackson.
When Eagles quarterback Michael Vick walked in late in the third quarter, fans began standing, section by section, as Vick walked around the court and took his seat.
The crowd chanted "MVP! MVP!" and Vick basked in the adulation, slapping hands with fans and waving to the crowd.
As the "MVP!" chants grew louder, Iguodala nailed a 23-footer for a 57-56 lead and the place went wild.
Iguodala hit a 3-pointer with 37 seconds left to send the Sixers into the fourth ahead 62-58.
The fun didn't last long.
Odum opened the fourth with consecutive three-point plays and Barnes' 3 gave the Lakers a 71-64 lead.
It wasn't all feel-good Philly: Jackson tweeted he was "watchn my lake show play the 2nd home town Sixers!!"
Jackson had to feel happy when Odom and Steve Blake hit consecutive 3s for an 81-68 lead and many of the same fans standing and cheering minutes earlier started to head for the exit.
Bryant was booed during pregame introductions, though not as voraciously as recently as two or three years ago. Sixers fans have softened their stance toward the star dubbed a "Hometown Zero" on the front page of the Philadelphia Daily News in 2007.
He donated more than $400,000 to his high school in Lower Merion and had the gym dedicated in his honor on Thursday.
He made just two baskets in the first quarter and didn't play at all in the second until there was 4:50 left.
Bryant wasn't needed early when the Sixers missed their first 11 shots. The Sixers turned a 44-39 halftime deficit into a third quarter lead once Iguodala got hot and the Lakers missed 17 of 23 shots.
Odom scored 11 points during the 27-8 spurt and that was enough for the Lakers to roll.
The Lakers went 24 of 28 from the free-throw line while the Sixers were 12 of 14. That was the only line each team mastered: Los Angles missed 12 of 15 3s and the Sixers missed 18 of 21.
Notes: Phil Jackson says his hometown school also named a gym after him, but "I didn't pay $400,000 for them to do it." Jackson also says Bryant can still shoot even as the years start to take a toll. "His offensive game is always going to be there. He can play in a wheelchair." ... The Sixers don't play at home again until Jan. 5.