Dwight Howard made 16-of-20 shots from the field and scored 36 points for the Magic, but he missed six straight free throws down the stretch to give the Raptors a chance.
Toronto cut a nine-point deficit to 87-85 thanks to Howard's struggles at the line, but Redick hit a 3-pointer with 10 seconds to go to boost the Orlando led back to five.
After Jose Calderon made a 3-pointer for the Raptors, Redick hit two from the foul line to wrap up the win. It was Orlando's third victory in four games.
Howard also had 13 rebounds and Ryan Anderson added 19 points and 13 boards for the Magic. Howard made just 4-of-14 free throw attempts.
DeMar DeRozan scored 23 points for the Raptors, who failed in their bid to win back-to-back games for the first time in more than a month.