Rookie Victor Oladipo contributed 16 points and six assists to help Orlando snap a three-game losing streak. Kyle O'Quinn had 14 points and 13 rebounds.
Kevin Love (back spasms), Kevin Martin (foot) and Nikola Pekovic (ankle) were out with injuries. Chase Budinger, starting in place of Martin, left in the first minute with an ankle injury and didn't return.
Orlando used a 10-1 late in the fourth quarter to finish off a second-half comeback in which the Magic rallied from 12 points down with five minutes to go in the third quarter.
The combination of sloppy ball handling by the Magic and Rubio having his way against a porous defense allowed the Timberwolves to build on a 48-46 halftime lead. Rubio had three assists and eight points in the run, including a driving layup that gave Minnesota a 72-59 lead, its largest of the game, with 4:45 left in the third quarter.
Rubio went to the bench and Minnesota's offensive rhythm went with him.
Oladipo and Harris took advantage, helping the Magic close to 77-72 by the end of the third quarter and open the final period with an 8-2 run. A steal and jam by Harris gave Orlando an 80-79 advantage with 8:38 left.
Oladipo followed with a 3-pointer, fed E'Twaun Moore for another 3 and O'Quinn finished the run with a jam to give Orlando an 88-83 lead with 6:44 to go.
Minnesota quickly reclaimed the lead, going ahead 89-88 on another drive through the lane by Rubio with 4:26 to go.
Oladipo drilled another 3 to start Orlando on the 10-1 run that ended with the rookie of the year candidate slicing through Minnesota's defense for a layup that made it 98-90 with 2:03 left.
Minnesota never got the deficit under six the rest of the way.
The teams traded shorts spurts of success at the offensive end in the first half that finished with Minnesota outscoring Orlando 19-5 in the final six minutes for a 48-46 halftime lead.
Jameer Nelson didn't hit a shot in the first half, and had only two points in the game, but had 12 assists, including seven in the first half as Orlando hit 20 of 41 (48.8 percent).
Afflalo carried the Magic in the first quarter with 10 points, but made only two shots in the second period and Orlando's offense stalled. The Magic were up 38-29 after a 15-foot jumper by Harkless, but didn't score for the next four minutes.
Harkless ended Orlando's drought with a driving layup, O'Quinn followed with a three-point play and Harkless hit a 3-pointer, but the Magic defense couldn't stop Rubio and still trailed by a basket at halftime.
NOTES: Backup F Shabazz Muhammad (knee) also sat out. . Magic C Nikola Vucevic (sore Achilles) missed his 20th game this season because of injury. Dewayne Dedmon got his first NBA start in his place. . Minnesota is 17-13 against the East this season. . Orlando improved to 6-28 in back-to-back games this season. Five of the six wins came in the second game. . Minnesota has lost six straight in Orlando.