With the Thunder leading by a point in the final 30 seconds, Kevin Durant missed a jumper. Victor Oladipo hauled down the rebound and led a fast break the other way.
Maurice Harkless took a pass under net and fed it to the trailing Harris, who followed with a two-handed slam to give the Magic a second straight victory.
He finished with 18 points and Arron Afflalo added 16 for Orlando, which roared back from a 16-point third-quarter deficit.
Oladipo and Glen Davis each registered 14.
Durant led the Thunder with 29 points and 12 assists.
Serge Ibaka contributed 26 points, six rebounds and five blocks.
Notable deaths of 2014 [PHOTOS]