It was the first career triple-double for Carter-Williams, who had earned NBA Rookie of the Month honors earlier Tuesday.
His tie-breaking free throw in the second overtime put the 76ers ahead to stay and he later added a lay-in for a 123-120 lead.
The Magic's Aaron Afflalo poured in a career-high 40 points but missed potential score-tying 3-pointer in the final seconds of the second OT.
Glen Davis provided 33 points and Victor Oladipo also registered a triple-double of 26 points, 10 assists and 10 rebounds.
Ray Liotta sues skin care company over use of likeness
Boston schools pull out free condoms over wrapping complaints