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.