The Magic held the Clippers to 16 points in the final period and finished the game on a 10-1 run for their third straight win.
Vucevic hit six free throws in the last 23 seconds to secure the victory and finished with 30 points and 21 rebounds. It was the second time in his three-year career he had reached 30 points and 20 boards in the same contest.
The Clippers overcame a 15-point halftime deficit by outscoring Orlando 32-15 in the third quarter, but could not sustain their momentum and had their three-game winning streak snapped.
Blake Griffin scored 23 points to go with 13 rebounds for the Clippers, who shot just 37 percent from the field. Los Angeles made only 3-of-19 shots from 3-point range.