Miller's brace maintained his 100% goalscoring record in the Scottish Premier League this season.
An own goal from Sean Dillon set the ball rolling early in the first half, before Miller doubled the advantage and Steven Naismith came off the bench to claim a goal of his own.
But it was Miller - who has found the back of the net in every league game so far this term, as well as scoring for Scotland - who had the final say with his eighth goal of the season.
This may not have been quite up there with the 7-1 thrashing handed out to United here last December but, following criticism over their negative approach against Manchester United, Rangers were more than satisfied with this outing as they move into pole position in the SPL.
Boss Walter Smith hinted he could freshen up his side following their exertions in the Champions League and Nikica Jelavic and Vladimir Weiss were both added to the team for the visit of United.
Jelavic is ineligible for the European competition and Weiss was an unused substitute at Old Trafford but both were back in the team for the clash at Ibrox, with Kirk Broadfoot and Naismith both dropping to the bench after their efforts midweek.
United also made a couple of changes from their win over Aberdeen last week, with injury doubts Craig Conway and David Robertson replaced by Scott Robertson and Paul Dixon.
Weiss weaved into the box from the left flank only to see his shot flash past the near post, with Dusan Pernis untroubled in goal.
But Rangers did not have to wait too long for the opener and took the lead after just nine minutes with some help from unfortunate United full-back Dillon who handed the home side the advantage.
Miller released Steven Davis down the right and he whipped a dangerous ball into the box intended for Jelavic.
But, as the striker stumbled and appeared to miss the opportunity, Dillon's attempts to clear saw him prod into his own net instead.
United could have levelled had Morgaro Gomis made more of his unchallenged run into the box but goalkeeper Allan McGregor dived low to smother at his feet before he could unleash the shot.
Rangers looked most likely to find the back of the net again and a cheeky back-heel from Miller was collected by Weiss, who bore down on goal only to drag across the face of goal and wide of the upright.
Madjid Bougherra supplied a cross from a tight angle at the back post but Pernis managed to punch to safety before Jelavic could connect with the header inside the six-yard box.
Jelavic then tried to turn provider when he squared across goal for the on-rushing Davis but Garry Kenneth was first to the ball to clear for a corner as Rangers failed to find a second goal before the break.
Jelavic netted his first goal for Rangers at Hamilton last week and was clearly desperate to add to that tally, stinging the palms of Pernis within seconds of the restart, before sending an over-head kick just over the crossbar.
He then met a Steven Whittaker cross in plenty of space with a firm header that fizzed narrowly past the goalkeeper's left post as the big forward continued to cause problems for the United defence.
Rangers pressed and Miller slipped a lovely pass through to Whittaker as he raced into the box with only the goalkeeper to beat but was wasteful with the opportunity and fired straight into the hands of Pernis.
Chances for Miller had been few and far between but his record in front of goal so far this season suggested he was always likely to pose a threat and he claimed his seventh goal in five SPL outings for Rangers after 69 minutes.
The Ibrox side's hard work paid off when Jelavic swept into the path of Miller as he raced into the box from the left and the goalkeeper had no chance as the striker lashed forcefully into the back of the net.
Maurice Edu then made way for Naismith and he bagged a goal of his own with 77 minutes gone. A Weiss corner was touched on by David Weir for Naismith to nod home at the back post and dash any hopes of a United comeback.
Miller was on the scoresheet again with eight minutes remaining.
Whittaker found Jelavic and he was once again the architect with a pass from the right for Miller to slot home with ease.