The Lakers entered the night a half-game ahead of Memphis, which had won 12 of 15, for the third spot in the West.
"They're a young team, they're hot, and they were coming for our spot," Bynum said. "We had to defend it, and we did that."
Pau Gasol added 14 points and eight assists for the Lakers, who won their third straight. Bynum and Bryant accounted for the Lakers' last 10 points after Steve Blake connected on a 3-pointer to open the second extra period.
Bynum went 15 of 18 from the field. Bryant said Bynum's performance was indicative of a change the Lakers have made in their offensive approach, running more things through the 7-foot center.
"The big games he had at the start of the season, he was having good games, but he wasn't being featured," Bryant said. "This is different. We're featuring him, and we're looking for him to make plays out of double-teams, and make plays for others, not just himself."
Marreese Speights led the Grizzlies with a season-high 25 points, while Marc Gasol finished with 20 points and 11 rebounds. Tony Allen had 18 points, and O.J. Mayo scored 14, but was 7 of 25 from the field. Mike Conley finished with 10 points and 11 assists for Memphis.
The Grizzlies took an early lead in the second overtime, but the Lakers clicked off six straight points, including a pair of baskets by Bynum, for a lead they wouldn't relinquish.
"We played a great game, and we should have won the game," Memphis coach Lionel Hollins said. "We had a few mental lapses at key times. As I'm always telling those guys, it's the small things that win or lose games."
Memphis played without leading scorer Rudy Gay, who was still suffering from concussion symptoms after a blow to the head in Sunday night's game at Denver.
The biggest difference in the game was at the free throw line, where the Lakers were 28 of 34, while Memphis hit all five of its free throws -- two of them on technicals called against Metta World Peace and Bryant.
According to the Elias Sports Bureau, the discrepancy in free throw attempts matched a Grizzlies franchise record dating to April, 1999, when the Seattle SuperSonics shot 29 more free throws than the then-Vancouver Grizzlies.
Memphis led 80-71 entering the fourth after outscoring Los Angeles 28-20 in the third behind 15 points from Speights. During that time, Memphis built its largest lead of the game at 72-55 just past the midway point of the period.
"I thought our guys a few times during the course of the ballgame could have folded," Lakers coach Mike Brown said. "That's just not in their makeup. ... There's never a panic with this group. The group just stayed the course, stayed the course and stayed the course."
Consecutive jumpers from Bryant cut into the lead early in the fourth, and when Bynum got free for an alley-oop dunk, the Lakers were within 88-86 with 5:40 left.
Speights scored on a rebound basket for a 95-90 lead with 2:28 left. But Bryant's 3-pointer tied the game at 95, then he fed Gasol for a dunk, giving the Lakers a 97-95 lead with 50 seconds left.
Marc Gasol scored inside for Memphis with 36.1 left, tying the game at 97 at the end of regulation.
Bynum's dunk with 1:20 left in overtime tied it at 103.
The Grizzlies carried a 52-51 lead into the halftime break on a 3-pointer by Quincy Pondexter with 26 seconds left after an intensely played first half that saw the Lakers commit 10 turnovers while shooting 50 percent.
Bynum was dominating inside, hitting 7 of 9 for 18 points. Bryant was 4 of 5, while adding 12 points.
The Grizzlies opened the second half on a 20-4 run, keyed by 13 points from Speights.
Then Memphis began misfiring and Bryant started to score. Allen, Memphis' top defender, was saddled with fouls and Pondexter had Bryant much of the time after intermission.
"The toughest thing defensively is not getting discouraged when he makes shots," Pondexter said. "We've all seen him through the years, and when he makes shots, you can't get discouraged."
But it was Bynum against Marc Gasol in a battle of Western Conference All-Star centers that was the most intense matchup. And, in the end, Bynum, who entered the game averaging 23.8 over the last four games, carried the night.
"They're trusting me now," Bynum said of his teammates. "They're just looking to get me the ball. When I get it, I'm doing decent things with it. Cutting down the turnovers. But it's part of learning and being a dominant player."
Asked how long Bynum can keep the pace, Bryant replied: "He can do it every night. He's been doing it every night."
Pau Gasol was booed like every other Laker in the pregame intros, despite his years in Memphis. ... Sam Young started in place of Gay. ... Derek Fisher's 3-pointer from the left corner with 5:16 left in the first quarter put him over 10,000 points for his career. ... The crowd of 18,119 marked the Grizzlies' third sellout of the season. ... Memphis lost for the first time this season after surpassing the century mark. The Grizzlies are 12-1 when scoring 100 points. ... The Lakers are now 8-14 on the road. They won at Minnesota on Friday and with the win over Memphis have consecutive road wins for the first time since Jan. 29 and Feb. 3. ... Memphis set a franchise record with 116 shots from the field, and it was a season high in the league.