The Magic broke open what had been a tie game by scoring the final 11 points of the third period and Los Angeles came no closer than five during the fourth quarter.
It was the 15th loss in 18 games for the Lakers, who will finish a seven-game road trip with a contest in New York on Sunday.
Harris came into the meeting with the Lakers averaging 13 points a game, but he hit 9-of-15 from the field and made 9-of-11 from the foul line.
Arron Afflalo added 23 points for the Magic, who won for just the second time in 14 tries. Orlando's 11 victories overall are the second fewest in the NBA ahead of only Milwaukee.
Orlando attempted 17 more free throws than did the Lakers and made 16 more.
Los Angeles was led by Pau Gasol with 21 points and 11 rebounds.