Paul Le Guen's side leapfrogged their opponents into second place in the table and now have their sight firmly fixed on European football for next season.
Aberdeen were put under immediate pressure when a Charlie Adam corner found the head of Nacho Novo whose downward header was gathered at the second attempt by Jamie Langfield.
Aberdeen looked to have gone ahead on 11 minutes when Darren Mackie gathered the ball on the byline. He set off on a terrific run which saw him beat three Gers defenders before smashing in a great left-foot shot from 20 yards that crashed off the post with Allan McGregor beaten.
On 13 minutes a Russell Anderson mistake was seized upon by Novo, but from the tightest of angles he clipped the ball over the advancing keeper and the crossbar.
Rangers opened the scoring on 22 minutes when Libor Sionko got the better of Richard Foster out on the right before picking out Novo whose looped effort somehow found the back of the net.
Minutes later and with the home defence missing in action, Novo returned the compliment by finding Sionko in acres of space and he had the simple task of sliding the ball into the unguarded net.
Neat interplay between Jamie Smith and Barry Nicholson saw the latter's snap-shot fly narrowly over the crossbar as the Dons tried to force their way back into the match.
In the final minutes of the half, the Dons nearly reduced the deficit but were again denied by the woodwork. Michael Hart's long ball through the middle was headed on by Lee Miller into the path of Mackie whose shot on the turn was blocked by Brahim Hemdani and back into the path of the big striker whose effort cannoned off the post and away to safety.
Dons skipper Anderson was narrowly off target on 58 minutes when his header from an acute angle fell just behind Mackie with the goal begging.
The visitors had another let off in the next minute when Alexander Diamond hooked Andrew Considine's free-kick back across the area for Scott Severin, who seemed only to need to knock the ball home, but Sasa Papac appeared from nowhere to hook the ball off his own line.
Aberdeen deserved to pull the goal back after 83 minutes when Mackie charged down and attempted clearance by Papac before driving in on goal. His shot was blocked by McGregor but the ball fell into the path of Steve Lovell who had the easiest of tasks to knock the ball home.