Steven Davis and Steven Naismith netted as the Scottish champions bounced back from their midweek European disappointment - and left the Dons still waiting to end their 20-year wait for a victory in Govan.
Rangers made two changes from the side which exited the Europa League to Maribor on Thursday night.
Naismith returned from suspension and youngster Ross Perry was added to the starting line-up, with Lee Wallace injured and Juan Manuel Ortiz dropped to the bench.
Carlos Bocanegra made his SPL debut from the start while fellow American Alejandro Bedoya was named on the bench.
Aberdeen were boosted by the return of Rob Milsom from injury but Darren Mackie had to settle for a place among the substitutes despite his winner against Dundee in the Scottish Communities League Cup midweek.
Isaac Osbourne was forced out of the action for the Dons for several minutes early on for treatment following a clash with Maurice Edu but Rangers failed to make the most of their numerical advantage before he returned sporting a bandage on his head.
The home side gradually began to apply pressure and Gregg Wylde should have done better with a shot that he dragged wide of the target.
Kyle Lafferty ran onto Nikica Jelavic's knockdown and raced into the box only to fire just over the crossbar.
Jelavic then set up Davis, who had better luck with a lofted effort that fell beyond the grasp of goalkeeper David Gonzalez and sneaked into the back of the net at the far post with 15 minutes gone.
Rangers could have doubled their advantage when Wylde delivered a tempting corner into the packed goalmouth where Dorin Goian rose above everyone else only to nod just over.
Aberdeen had so far failed to pose any problems for the opposition defence and Kari Arnason tried his luck with a shot from 25 yards that fizzed well wide, with Allan McGregor untroubled in the Rangers goal.
At the other end, Maurice Edu went to ground in the box under pressure from Youl Mawene but contact was minimal and the American then sent a header flashing past the post after connecting well with a cross from Wylde.
Rangers made a change on the stroke of half-time when Goian was replaced by Steven Whittaker, who had been sidelined with a broken toe.
Aberdeen could have been back on level terms just after the restart when Scott Vernon took advantage of a mix-up between Perry and Bocanegra and burst into the box only to find himself forced too wide to unleash the shot.
Wylde saw a long ball from the left-flank bounce off the bar on the way over as Rangers tried to pile on the pressure and add to their first half opener.
Jelavic then collected a nod down from Edu and should have scored but rifled across goal and past the upright.
Rangers were almost left to rue those missed opportunities, when McGregor was called into action to palm a Vernon shot to safety, before Richard Foster's diving header crashed off the crossbar.
Bedoya was handed his Rangers debut when he replaced Lafferty with a little more than 20 minutes to go, to loud applause from the Ibrox crowd.
Aberdeen pushed forward in search of a late equaliser but lacked a cutting edge in front of goal and struggled to carve out any real chances.
Davis could have added to his tally for the day but his effort was blocked by Osbourne, before Naismith lashed home from close range after Gonzalez fumbled a Davis free-kick in injury time.