Deron Williams also had 17 points, five assists and four steals for the Nets, whose victory gave them a two-game lead for the fifth spot in the Eastern Conference playoff race over the idle Washington Wizards.
Tobias Harris came off the bench to lead the Magic with 18 points, who have lost their last two games.
Trailing 59-55 with 6:59 remaining in the third quarter, Brooklyn went on an 13-0 run, highlighted by five points from Teletovic, to take a 70-59 lead with 3:23 left in the quarter. Ronnie Price then hit a 3-pointer to end Orlando's scoring drought.
Brooklyn coach Jason Kidd pulled most of his regulars after the end of the third, leading 79-70. But Kidd was then forced to bring most of them back after Orlando scored six straight points to pull to 87-81 with 5:27 remaining.
Kidd called a timeout soon after and the Nets responded with a 10-3 run to extend the lead to 97-84 with 1:07 to go.
Orlando led throughout most of the first half, shooting 54 percent from the floor, good enough for a 49-46 lead at halftime.
NOTES: Brooklyn C Brook Lopez, who broke his foot earlier this season, greeted fans on Fan Appreciation Night. Lopez, who fractured the fifth metatarsal bone in his right foot during a game on Dec. 20 at Philaldephia, watched from the bench. Lopez also had a procedure on March 3 to repair a torn tendon and tighten the lateral ligaments in his left ankle.