Kobe Bryant led the Lakers with 29 points but he and Los Angeles were nowhere near as dominant as they were in a Game One 100-75 thumping of the Magic, who could have won in regulation had Courtney Lee's lay-in attempt at the buzzer not rimmed out.
"We just drove ourselves through the game," Lakers coach Phil Jackson said. "I didn't think Kobe had a good game at all as far as his standards go.
"They double teamed him, they trapped him, they came on all his drives, and we didn't adjust to it."
Pau Gasol, who had 24 points and 10 rebounds, scored seven of the Lakers' 13 points in the overtime to key the victory. He hit seven-of-14 shots overall and 10-of-11 from the line.
The best-of-seven series now shifts to Orlando for the next three games, if necessary. Game Three is on Tuesday and Orlando coach Stan Van Gundy is looking for a turnaround.
"You know, series can change," he said. "You've got to take it one game at a time. It's extremely frustrating not to have gotten tonight's game because I thought we fought hard.
"I didn't think we played great because we had 20 turnovers but we fought hard. We had chances to win. We didn't get it done."
Both teams had chances to win the game in regulation, Bryant squandering an opportunity when his short jumper with 0.6 seconds remaining was blocked by Hedo Turkoglu.
After a timeout, the Magic delivered an alley-oop pass to Lee, whose potential series-tying shot at the buzzer bounced off the rim.
"I was obviously relieved when he missed that shot because it could have been a heartbreaker, and right now we could be in a totally different situation," Gasol said.
"I was surprised he was kind of wide open."
The Lakers outscored Orlando 13-8 in the extra session to remain on track for their 15th NBA title and first since 2002.
Orlando was paced by Rashard Lewis's 34 points on 12-of-21 shooting, while Turkoglu added 22. The pair hit a combined five-of-21 shots in the opener but nailed 20-of-38 on Sunday.
"I don't think we dodged a bullet," said Bryant, who had 40 points in Game One.
"They played extremely well and we played well enough to win. They bounced back like we knew they would, played extremely well, and we got out of here with a win."
All-Star center Dwight Howard had 17 points and 16 rebounds for the Magic but cost his team dearly with seven turnovers. Each time he put the ball on the floor, several Lakers were swatting at it.
"I've just got to do a better job of finding my team mates and being aware of the guards coming in the paint for strips," he said.
"As a team we've just got to do better with not turning the ball over.
"That's how they got going on the offensive end, because of our turnovers, and it gave them the game tonight."