The visitors had the majority of the ball in the opening 10 minutes, but it was Hearts who had the first real chance of the match when Jamie Walker burst through, rounding a couple of defenders before seeing his shot kept out by Cammy Bell.
Despite the home side's strong start, it was Rangers who opened the scoring just after the half-hour mark when Nicky Law curled a free kick into the box, leaving Darren McGregor to nod it in at the far post.
Haris Vuckic tried to create a second for Stuart McCall's side just a few minutes later, but there was no-one there to meet his cross, allowing Hearts to break on the counter-attack, but they could not force an equaliser.
Rangers doubled their advantage shortly before the break as Law and Vuckic played their way down the right before the latter cut the ball back for Miller, leaving the striker to smash it in from close range.
However, with Hibernian currently ahead in their final fixture, it does not look like victory will be enough to move Rangers up to second in the table. body check tags ::