Rangers went ahead shortly after the interval when Jean-Claude Darcheville forced the ball home from close range before Kris Boyd secured the points when he shot home from six yards.
This win keeps Rangers within four points of Celtic as the battle for the title once again looks set to go to the wire.
Aberdeen forced some early corners and Mark Kerr's drive went narrowly wide.
It took Rangers some time to get into the match but a swift break by Pedro Mendes and Kyle Lafferty ended with Boyd hitting his first-time effort just wide.
Barry Ferguson headed just wide from Darcheville's cross before Aberdeen nearly took the lead just before half-time.
From Sone Aluko's cross Gary McDonald's ten-yard shot was brilliantly parried by Allan McGregor in the Rangers goal.
Jamie Langfield then did well to touch over a wayward header from Andrew Considine.
Shortly after the break the Aberdeen keeper did well to keep out Darcheville's shot from Boyd's flick while at the other end Lee Miller's flashing drive was just off target before Rangers took the lead.
Charlie Adam's corner was blocked at the far post and, although Boyd's effort was also cleared, Darcheville managed to squeeze the ball home from six yards.
Aberdeen nearly drew level but Alexander Diamond's header from Derek Young's corner was headed off the line by Mendes.
Rangers doubled their lead in the next minute when another Adam corner was prodded home by Boyd.
Adam's free-kick then shaved the post and Langfield did well to parry Lafferty's shot before Kerr pulled his shot wide for the visitors near the end.