Glen Davis had 19 points, and Arron Afflalo and Victor Oladipo each added 18.
The game was the first meeting between rookies Michael Carter-Williams and Oladipo, and both played big roles.
The Magic led by 15 points before fighting off several second-half surges by the Sixers, which they beat for 17th time in 20 meetings.
Thaddeus Young led Philadelphia with 26 points and Carter-Williams added 23. It was Young's first game in a week after missing three games while dealing with a death in his family.
The 76ers have now lost two straight and six of their last seven.
The Magic saw what had been a 15-point first-half lead dwindle to a point early in the third quarter.
The lead was 85-83 before Afflalo's three-point play gave Orlando a little breathing room with 6:49 to play in the game.
The 76ers kept coming before Afflalo struck again and turned a Philadelphia turnover into a layup that made it 93-87.
That was followed a few possessions later by a 3-pointer by Oladipo that put the Magic up 98-89 with three minutes remaining to end the threat.
Philadelphia got welcomed news shortly after their arrival in Orlando Wednesday when Young rejoined the team during the team's morning shoot around.
76ers coach Brett Brown said the plan going forward was to ease Young back into things slowly following his absence.
Young didn't start, but entered the game for the first time at the 7:42 mark of the first quarter and immediately started to make an impact.
Despite the victory, the Magic continued to deal with the injuries on Wednesday.
Point guard Jameer Nelson left the game in the second quarter and did not return after limping off with a sprained left foot.
Also, after making his season debut Sunday against Phoenix, Magic forward Tobias Harris sat out his second straight game with soreness in his left ankle.
Harris was supposed to make his first start of the season against Atlanta Tuesday night, but was scratched just before tip-off. The ankle has now kept him out of 14 of the Magic's 15 games this season.
Magic coach Jacque Vaughn said there was no update on Harris' status other than that the team would see how he responded to treatment.
It was 55-50 at halftime as the Magic - riding Vucevic's 17 points and 10 rebounds - dominated the first 21 minutes of the first half and built a 15-point lead. He went right at Philadelphia's Daniel Orton, and hit his first eight shots of the night.
It nearly evaporated in the final three minutes of the half, though, as the Sixers closed with a 10-0 run that included eight points by Young.
Philadelphia's spurt included three Magic turnovers. Orlando had seven turnovers in the second quarter alone, putting a damper on a half in which Orlando shot 54 percent from the field and held a 28-12 scoring advantage in the paint.
NOTES: Davis made his second start of the season and appeared in his fourth game of the year since missing the first 11 games of the season with a broken bone in his left foot. ... Sixers F Spencer Hawes missed his second straight game with soreness in his left knee. ...Brown who coached Magic coach Vaughn as a player and later alongside him as fellow assistants in San Antonio said he's impressed with how he's adapting to the job. "The speed of it maybe caught people off guard, but I think the selection has been confirmed that it was a smart decision to grow with Jacque." ...Referee Tre Maddox left the game in the first quarter with an ankle injury.