Harris finished with 25 points and 11 rebounds while Vucevic had 22 and 10 for Orlando, which picked up its first win over a winning team since upending the Pacers on Feb. 9.
Victor Oladipo donated 13 points, six assists and five boards and helped hold Damian Lillard to 17 points on 17 shots.
Despite their poor record, the Magic showed they were no pushover by scoring nine of the game's first 11 points. The Blazers called timeout to turn the tide, and their subsequent 15-4 run gave them their first lead.
Portland led 26-23 at the end of the first and was in front by six midway through the second before another Orlando run, this time a balanced 16-0 flurry, yielded the first double-digit margin of the game at 48-38.
Oladipo highlighted the stretch with a crossover that sent Mo Williams back pedaling to the hardwood before finishing with a floater over Lopez while being fouled.
The hosts went into the break holding a 50-42 lead, and turned it up another notch after the Blazers pulled within two early in the third. Harris and Maurice Harkless kicked in consecutive 3-pointers for a 62-54 lead, and a Vucevic layup off a nifty bounce pass from Oladipo rebuilt Orlando's 10-point lead.
An Oladipo dunk in the final minute of the third sent the Magic into the final stanza with a healthy 79-65 advantage, and the difference never dipped below 10 the rest of the way.
2014: The Year in Music [PHOTOS]