Fir Park had not been a happy hunting ground for the Scottish champions in recent seasons but a double from Miller, an own goal from Steven Saunders and a Vladimir Weiss strike sealed the win, with John Sutton's effort nothing more than a consolation for the Steelmen.
Motherwell had managed to beat the weather to ensure this clash went ahead amid further fixture chaos caused by the weather but failed to beat their visitors as Rangers strengthened their grasp on top spot with their first SPL victory at this venue since January 2, 2007.
Motherwell made one change: Steve Jennings was suspended following his red card against Hearts and replaced by Saunders.
Rangers named an unchanged side from the one who drew with Inverness in their last outing. Both Kyle Lafferty and Maurice Edu failed to make the squad despite hopes of a return from injury for the duo.
Walter Smith's men had the best of the chances in the opening spell and looked dangerous when Steven Naismith embarked on a surging run from his own half before picking out Richard Foster.
Foster attempted to set up Steven Whittaker at the back post but his effort was blocked by the Motherwell defence and the chance was lost.
Whittaker then turned provider for Miller who bore down on goal from a tight angle only for goalkeeper Darren Randolph to race off his line and block well.
The ball broke for Naismith but his close-range header was nodded off the line by Mark Reynolds, hitting the crossbar on the way over as the home side breathed a sigh of relief.
A Lee McCulloch shot was then helped towards goal by Naismith only for some more last-gasp defending from the home side keeping the scoreline level, this time Keith Lasley hooking off the line.
Rangers had looked more likely to open the scoring and their pressure paid off when they surged into the lead with 26 minutes gone.
Madjid Bougherra collected from Naismith on the right wing before supplying the cut-back for Miller and all that was required was a simple finish from the striker who lashed home from 12 yards.
Rangers doubled their lead after 33 minutes when Weiss delivered a dangerous free-kick into the packed box and the unfortunate Saunders nodded past Randolph into the back of his own net.
Both teams were forced to make a change five minutes before the break after Naismith and Tom Hateley both pulled up and were replaced by John Fleck and Sutton respectively.
Motherwell failed to pose a threat in front of goal in the first half but hauled themselves right back into the game when they pulled a goal back a minute after the restart.
Bougherra and David Weir both failed to deal with a long ball from Randolph, allowing Sutton to snatch possession and poke into the bottom corner.
But Rangers restored their two-goal lead just five minutes later when Weiss weaved past several players and into the box before slotting coolly past the goalkeeper from 10 yards.
Weiss was then the architect for Miller's second of the day after 61 minutes. Miller connected awkwardly with the free-kick but did enough to bundle over the line at the near post, with Randolph no doubt feeling he should have done better.
With little hope of a comeback from Motherwell, Rangers were able to withdraw Weiss and hand some game-time to youngster Jamie Ness.
The game had begun to fizzle out in the latter stages but Steven Hammell tried his luck with a cross come shot that Allan McGregor collected comfortably.
The 4-1 win provided the best possible boost for Rangers ahead of next week's Old Firm derby when Celtic travel to Ibrox on January 2.