Elfrid Payton, who set up Vucevic's winning shot with an inbounds pass, scored or assisted the Magic's final six baskets as they won for only the third time in 18 games in 2016.
The Magic had gone scoreless since Payton's jump shot with 3:41 left, squandering a 94-86 lead.
Big starts by Fournier and Vucevic, along with seven Atlanta turnovers, staked the Magic to an early 14-point lead, and Orlando led 48-41 after a first half in which the Hawks shot 34 percent (14 for 41).
The margin was back to 14 until Atlanta's Thabo Sefolosha finished the third quarter with a 3-point bank shot from beyond the mid-court line.
Teague scored seven of nine straight Atlanta points early in the fourth quarter, and a 3-pointer by Bazemore with 48 seconds left pulled the Hawks even for the first time since their 4-2 lead in the first minute.
Hawks: C Tiago Splitter sat out a fourth straight game with a hip injury and will rest through the All-Star break.
Magic: F Tobias Harris, who took stitches in his head after a collision in the fourth quarter Friday night, missed his first game of the season with a sore left ankle.
The Magic and Hawks play in Atlanta on Monday night.