Harris led five Magic players in double figures with 18 points. Kevin Durant scored 29 with 12 assists for the Thunder, which also got 26 points from Serge Ibaka.
The victory marks Orlando's fourth straight at Amway Center, establishing a new best in the coach Jacque Vaughn era.
Durant took over the game in the first quarter, scoring 15 points and accounting for six others via assist as OKC staked itself to a 36-23 lead. The league's leading scorer shot 5-of-7 in the period despite reasonably solid defense from Harris, and he did a brilliant job reading the Magic's help defenders and finding the open man.
And the open man, whoever he was, converted: Oklahoma City shot 70 percent in the first quarter.
Harris, for his part, played a more assertive offensive game than he has in recent weeks, attacking the rim off the dribble. As a result of that approach, Harris managed 10 first-quarter points on 4-of-9 shooting, with Ibaka and Kendrick Perkins blocking him once apiece at the rim.
Three-pointers helped the Thunder maintain control of the game in the second despite their five turnovers leading to eight Orlando points. OKC went 5-of-6 from deep in the period even without Durant attempting a single shot outside the arc.
Oladipo, who didn't play in the first quarter, came off the bench firing in the second, going 3-of-3 for nine points in his nine minutes as the Magic's second unit again gave it a lift. The Thunder built a 14-point halftime lead regardless, however.
Orlando worked its way back into the game in the third quarter behind Glen Davis, who scored 10 points in the period. A deep Jameer Nelson triple at the 3:54 mark brought the Magic to within six, a margin they'd reach twice more in the quarter before finishing it down eight. Oklahoma City appeared to ease off the proverbial gas after its strong first half, coasting by on its talent advantage and its hot outside shooting.
That trend continued in the fourth quarter, which Orlando opened on a 13-4 run. The Magic could have built an even bigger advantage had they not missed three free throws early in the period, but they were bound to miss some freebies eventually: Orlando entered the fourth a perfect 15-of-15 from the line.
A difficult Harris shot in traffic put Orlando up by four points with 6:07 to play, but Jackson tied the game less than two minutes later with back-to-back jumpers, the second of which occurred as Oladipo protested a no-call after crashing to the court on a layup try seconds earlier.
With the score knotted at 99, Durant drove the lane in transition and found Thabo Sefolosha spotted up in the left corner for three, giving the Thunder the lead.
Orlando committed a five-second violation after a timeout, but the Thunder bailed it out on the next play as Sefolosha crashed into Davis for a charge, keeping the Magic's hopes alive. After drawing a three-shot foul on Ibaka, Arron Afflalo made two free throws to bring Orlando to within a point with 55.2 seconds remaining.
Durant missed a clinching jumper with four seconds to play. Oladipo snared the rebound and advanced it to Maurice Harkless, who flipped the ball back to Harris for the winning dunk just in the nick of time.