Rising star Wagner took full advantage of wayward Lakers shooting from the free throw line in the closing seconds of a see-saw battle at the Crypto.Com Arena to give Orlando a hard-fought win.
Wagner, 23, finished with 37 points, 11 assists and six rebounds to lead the Magic scoring, with older brother Moritz adding 19 from the bench and Jalen Suggs scoring 23.
The in-form Lakers, who had gone into Thursday's encounter on a six-game unbeaten streak, were left ruing some wasteful shooting from the free throw line in the fourth quarter, where they made just three of nine attempts.
The Lakers had looked poised to close out the win after opening up a four-point lead with 27 seconds remaining at 118-114.
But Franz Wagner closed the gap to 118-116 with a driving layup, and then Anthony Davis missed two free throws to give Orlando a glimmer of hope with 19 seconds remaining.
Wagner then punished the Lakers profligacy, coolly knocking down a step-back three from 26 feet to give Orlando what turned out to be the winning lead.
Davis led the Lakers scorers with 39 points while LeBron James finished with 31 points, 10 rebounds and seven assists. Rookie Dalton Knecht added 17 points.
Orlando improved to 10-7 while the Lakers slipped to 10-5 and are now fourth in the Western Conference.
In other games, the San Antonio Spurs improved to 8-8 for the season after scrapping to a 126-118 win over the Utah Jazz.
Utah had seemed poised to claim only their fourth victory of the season after surging into a 20-point lead in the second quarter against a Spurs side missing the injured Victor Wembanyama.
But San Antonio erupted for 75 points after half-time to outscore Utah by 24 points and snatch victory.
Harrison Barnes led San Antonio's scoring with 25 points and 10 rebounds while rookie Stephon Castle and Zach Collins added 18 points each on a night when eight Spurs players finished in double figures.
Lauri Markkanen scored 27 points for Utah, who slipped to their fourth straight defeat.
In Charlotte, Brandon Miller produced a flurry of scoring in overtime to finish with a career-high 38 points as the Hornets defeated the Detroit Pistons 123-121.
Miller rattled in eight overtime points to help Charlotte claim a win which improves their season record to 6-9.
The Toronto Raptors (4-12) upset the Minnesota Timberwolves, winning 110-105.
