Second-half goals by Lee McCulloch, Steven Naismith and substitute Kris Boyd were more than enough to see off a weak Dons challenge.
After their Champions League win against Stuttgart on Wednesday night it was understandable that the Gers were slow out of their blocks. Naismith was making his debut and his pace troubled the visitors' defence all afternoon.
Early on Daniel Cousin flicked a header on to Naismith who laid the ball back to McCulloch whose powerful drive went narrowly over.
Aberdeen were holding their own in a lacklustre first half and Chris Maguire made a run ending with a shot just off-target. Scott Severin then took a quick free-kick, but Andrew Considine could only shoot into the sidenetting.
Severin then went close when he drilled a 20-yard shot narrowly wide of Allan McGregor's right-hand post.
Perhaps inspired by news of Celtic's defeat at Easter Road, Rangers took the lead in the first minute of the second half. McGregor's long clearance was chested down by Cousin to McCulloch whose dipping shot from 30 yards beat Jamie Langfield all ends up.
Rangers stepped up the pressure and Alexander Diamond was lucky not to concede an own goal with a wild clearance which ended on top of the net.
Langfield made a superb save to touch over Steven Whittaker's rasping volley and from Barry Ferguson's corner Cousin glanced his header just wide of the far post.
Naismith added Rangers' second with a superb goal. Latching onto a Sasa Papac pass, the ex-Kilmarmock striker cut inside Michael Hart before curling his shot into the far corner from almost on the byline.
It was all Rangers now and Ferguson nearly added a third with an audacious 45-yard shot when Langfield mis-hit the clearance.
Aberdeen resorted to some strong-arm tackles in the closing minutes with Diamond's tackle on Naismith, which led to the striker limping off, being particularly cynical.
Rangers added a third through substitute Boyd, who powered home with his left foot a Jean-Claude Darcheville pass to finish off a good few days for the Ibrox club.