The victory may not have been quite as emphatic as Celtic's 9-0 thrashing of the Dons seven days ago but was enough to allow the Scottish champions to increase their lead at the summit to four points.
Goals from Kenny Miller and Vladimir Weiss sealed the win for Walter Smith's men, albeit Miller failed to covert from the penalty spot just before the interval.
Rangers made three changes from the side who lost to Hibernian in midweek for the visit of Aberdeen. Sasa Papac and Maurice Edu were both injured, with John Fleck, Weiss and Kirk Broadfoot added to the team.
Kyle Lafferty apparently picked up an injury in the warm-up as Rangers named just six substitutes.
Aberdeen were boosted by the return of skipper Paul Hartley but Darren Mackie missed out through injury and Andrius Velicka was ineligible under the terms of his loan deal.
Rangers had the best of the chances early on, with Weiss trying his luck with a shot that was smothered at the near post by goalkeeper Jamie Langfield.
Steven Davis then set up Lee McCulloch for a header from point-blank range that the goalkeeper did well to block.
Steven Naismith picked up the first booking of the game for a challenge on Chris Maguire, before Steven Whittaker rippled the side netting with an angled drive.
The breakthrough came after 22 minutes when Weiss cut inside from the left and lofted into the path of Miller who sent a back header past the grasp of Langfield.
Maguire followed Whittaker into the referee's book for a foul on Weiss, before Rangers doubled their lead after 32 minutes.
Miller's cutback found Fleck in the box but his effort was blocked before falling for Weiss to unleash a ferocious shot that took a slight deflection before nestling in the bottom corner.
Rangers should have increased their lead further four minutes before the break when referee Calum Murray pointed to the spot after Zander Diamond fouled Whittaker in the box.
Miller stepped up for the spot-kick, looking for his 16th of the season, but Langfield did well to dive to his left and punch to safety.
Aberdeen tried to win a penalty of their own shortly after the restart when Scott Vernon went to ground under pressure from Madjid Bougherra but the referee ignored the claims.
Miller could have made amends for his poor spot-kick attempt with a well-struck shot that fizzed across the face of goal and just past the post.
Langfield was then called into action to block a powerful free-kick from distance from Weiss, with the winger also keen to add to his tally for the day.
Rangers were desperate for the third goal to snuff out any hope of a Dons comeback and Bougherra found Miller with a lovely long ball and the striker looked set to add to his tally only for Langfield to come to the rescue.
Miller then spurned another decent chance when he collected a chipped cross from Whittaker only to stab wide from just six yards out.
Weiss was replaced by Gregg Wylde with 15 minutes to go and the youngster was not too far away when he met a long, low corner from Fleck and rifled just over the crossbar.
Rangers were able to hold on for the win, while Hamilton's defeat to Inverness prevented Aberdeen from slipping to bottom of the table.