Kyle Lafferty set the ball rolling in the 54th minute and Miller wrapped up the points from the penalty spot six minutes from time, shortly after the luckless Kris Boyd was substituted - the latter's search for his 100th SPL goal for the club continues.
Celtic's win over Hibernian 24 hours earlier ensured there would be no title party but the Scottish champions can secure the silverware at Hibs next Sunday - or without even kicking a ball should the Hoops lose to Dundee United earlier in the day.
Boyd was restored to the Rangers team as Walter Smith made two changes from their goalless midweek draw at Dundee United.
The striker returned to the starting line-up along with Kevin Thomson for the clash at Ibrox. Steven Naismith and Maurice Edu - who limped out of Wednesday's game at Tannadice - were both named on the bench.
Hearts also made two changes from the side which defeated Kilmarnock, with Ismael Bouzid making his long-awaited comeback and Craig Thomson also starting for the Jambos.
Jamie MacDonald was called into action early on when Madjid Bougherra burst down the right flank before whipping a dangerous cross-cum-shot into the box that the Hearts goalkeeper just managed to tip over the crossbar.
David Weir then had an unlikely chance to open the scoring for the champions when a short corner broke to him 30 yards out, but the veteran defender ballooned well over.
At the other end, Craig Thomson's cross found Suso Santana but he bulleted his header well wide of target.
Rangers continued to press and Lee McCulloch forced a save from MacDonald, before he spilled a Steven Davis free-kick only to recover and smother before anyone could pounce on the rebound.
With half-time fast approaching and still no goals, Rangers increased the pressure and Miller embarked on a great run before attempting to set up Boyd in front of goal, but Marius Zaliukas made a timely intervention and the chance was lost.
Bougherra then picked out Boyd in the box and he nodded on for McCulloch but his powerful shot failed to break through a cluster of maroon jerseys, amid claims of handball from the home side.
Rangers looked hungrier in the second half and Miller was unfortunate not to find the back of the net shortly after the restart.
A long ball from Sasa Papac picked out the striker and his header appeared netbound before MacDonald threw himself across goal and clawed the effort past the post.
The breakthrough came after 54 minutes when Kevin Thomson's corner found Lafferty who bulleted a near-post header past the Hearts keeper, with his efforts to block proving fruitless.
Rangers could have doubled their advantage when Kevin Thomson collected a short ball from Davis before sending a lovely curling effort inches over the crossbar.
Hearts skipper Michael Stewart came off the bench to end almost two months on the sidelines, while Boyd was withdrawn for Nacho Novo with just over 10 minutes to go.
He would have been rueing the timing of his withdrawal when Naismith was pushed in the box by Eggert Jonsson and referee Iain Brines pointed to the penalty spot before handing the Hearts man a straight red card.
In the absence of their top goalscorer, it was Miller who stepped up for the penalty and, despite getting a hand to the shot, MacDonald could not prevent the ferocious effort from finding the back of the net with six minutes to go.