He thinks that team success could be coming soon.
"To me, it's just about us getting healthy, putting it together and getting some consistency," Afflalo said. "I feel once we get consistent with the things that we do well, we're going to be pretty good."
Davis had 14 points and 11 rebounds despite playing with a sore left shoulder, powering Orlando to a 54-45 edge on the glass in just its second win in the past 10 games. Vucevic finished with 10 points and 11 boards.
Orlando (8-17) closed out a nine-game stretch that included eight road games. It begins a six-game homestand Wednesday night against Utah.
"I'm really looking forward to our personal home stretch back in Orlando and hopefully putting a streak together for once," said Afflalo, who is averaging a career-high 21.6 points per game on 47 percent shooting.
The Bulls (9-14) had a chance to win despite shooting 34.6 percent from the field during another terrible offensive performance. Trailing 81-79 with 6.8 seconds left, Joakim Noah made a terrific bounce pass to a streaking Luol Deng, but he missed the easy layup.
"I had a good angle, and it was a great pass by Jo," Deng said. "I missed the shot and I knew I missed it when it left my hand. It was just a bad, bad miss and my fault."
Davis grabbed the rebound and made two foul shots to give the Magic a four-point lead that proved crucial when Mike Dunleavy made a 3-pointer from half court as time expired.
Deng had 26 points and eight rebounds for Chicago, which has dropped five of six. D.J. Augustin and Dunleavy had 14 points apiece, and Noah finished with 13 points and eight rebounds.
"It's not pretty right now," Dunleavy said. "We are battling, we are trying, we just keep coming up short."
Jameer Nelson had 14 points and seven assists for Orlando, which had lost its previous five games against Chicago.
The Magic appeared to be on their way to an easy victory when Vucevic and Afflalo made consecutive jumpers to make it 63-46 with 5:17 left in the third. Afflalo had 13 points in the period.
But the Bulls started to pick up their play at the end of the quarter. Augustin, Dunleavy and Deng each made a 3-pointer during a 13-2 run that trimmed Orlando's lead to 65-59 with 58.1 seconds left, capped by an emphatic two-handed jam by Taj Gibson over Vucevic.
"It's tough. We're losing to teams that we're supposed to be beating," Gibson said. "That's the way I feel. I just feel like we have to do better, including myself. This one hurts."
The Bulls played without point guard Kirk Hinrich for the second straight game due to back stiffness. Coach Tom Thibodeau said he hopes Hinrich will be able to return soon.
Marquis Teague replaced Hinrich in the starting lineup, but Chicago's offense looked much better when Augustin was on the court. Augustin, who signed with the Bulls on Friday and started the second half, had eight assists in 37 minutes, while Teague was scoreless in 11 minutes.
Thibodeau said he thought about starting Augustin but he wasn't sure whether he was comfortable enough with the Bulls' schemes.
"I didn't want him to be tentative," Thibodeau said. "I thought he was much more aggressive. I liked the effort that he put in defensively. I think there are things he can do better, but I thought he made great effort and I think that's important."
Davis injured his shoulder in the fourth quarter of Orlando's 101-98 loss at Oklahoma City on Sunday. He was a game-time decision against the Bulls, but he made two big jumpers in the final period while playing 33 minutes.
"I'm just proud of our guys, to go back home with a win," he said.
Davis said his shoulder loosened up during the game and he just tried to give it everything he had. He also said he wanted to play against Bulls forward Carlos Boozer.
"I like playing against Boozer. He really fires my engine," Davis said with a wry grin. "Just his whole attitude really gets under me."
Magic rookie Victor Oladipo, who played his college ball at Indiana, received a warm ovation when he was introduced with the starting lineup. ... The Bulls waived G Mike James before the game. He played 37 1/2 minutes over seven games with Chicago. ... These teams play again Jan. 15 in Orlando and April 14 back in Chicago. ... Boozer had six points on 3-for-10 shooting to go along with 13 rebounds.