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.
The game was the first meeting between rookies Michael Carter-Williams and Oladipo, and both played big roles. Oladipo registered a season-high 42 minutes.
Though both had their highlights, it was how Orlando played together down the stretch that stuck out more.
The Magic saw their double-digit, first-half lead dwindled down to a point early in the third quarter.
It was 85-83 when 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 and ended the threat.
"We had a pretty impressive win (Tuesday) night (at Atlanta)," Afflalo said. "We hadn't had the best track record of backing up good victories with solid, back-to-back victories on back-to-back nights. It got a little ugly there in the second and third quarters, but we showed a little mental toughness and got us a good victory."
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.
"They did a good job tonight of keeping the lead," Young said. "Once they got it, we'd make a run to take the lead and they would (answer with) five or six points. They just kept their foot on the gas and kept moving."
76ers coach Brett Brown said the plan going forward was to ease him 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.
"I didn't want to start him; I didn't know how long I was going to play him," Brown said. "You just go by gut feeling and judgment, and it was clear right from the get-go that he had bounce, he had energy, he wanted to play. He was good. So he ended up with (29) minutes, which I would not have guessed at the start of the game."
The 76ers have now lost two straight and six of seven.
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.
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.
Vucevic said he hopes the win will help the Magic to begin to play with a lot more consistency.
"We made improvements, but we've still got a ways to go," he said. "We can't have streaks when we lose four or five games in a row. It's hard to make up for those. So we gotta try to be more consistent. We can't win every game ... but we gotta try to play the way we played the last two games."
Referee Tre Maddox left the game in the first quarter with an ankle injury. ... 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.
Follow Kyle Hightower on Twitter at http://www.twitter.com/khightower
Copyright by STATS LLC and The Associated Press
ORLANDO, FL - NOVEMBER 27: Maurice Harkless #21 of the Orlando Magic shoots a foul shot against the Philadelphia...
MVP: You can't help but wonder what Philly fans think when they see ex-Sixer s center Nikola Vucevic (21 points, 16 rebounds, 5 assists, 3 blocks) put up big numbers, especially when it happens against the Sixers.
X factor: After a slow start to the game, Arron Afflalo came alive in the fourth quarter. He scored 11 of his 18 points in the period and helped pave the way for Orlando to come away with a victory.
That was ... a dud: Victor Oladipo, who originally got the starting nod at shooting guard, saw some time against Michael Carter-Williams in this game after Jameer Nelson went down with a sprained left foot. But there weren't much fireworks between the two.