The managerless visitors took the lead on 14 minutes through Danny Wilson's looped header into the far corner of the net from 16 yards.
Former Dons midfielder Ryan Jack was sent off after the break, but Josh Windass fired Rangers further in front on 63 minutes, connecting with a Daniel Candeias delivery to rifle home from close range.
Rangers, however, were able to hold on for all three points, putting them level with Aberdeen but above them in the table on goal difference.
Aberdeen (4-2-3-1): Lewis; Logan, O'Connor, McKenna, Considine (Harvie 81'); McLean, Shinnie; Stewart, May (Maynard 62'), Wright (Ross 52'); Rooney
Rangers (3-4-3): Foderingham; Wilson (Cardoso 45'), Bates, McCrorie; Tavernier, Jack, Holt, John; Miller, Pena (Candeias 58'), Windass (Herrera 90+4')