Kyle Lafferty, Steven Davis and Nikica Jelavic grabbed a goal apiece at Fir Park and Steven Naismith claimed a brace as the Scottish champions stretched their lead at the summit to four points.
The onus is now on Celtic to respond to the pressure and put points on the board against Dundee United on Sunday and make the most of their game in hand at Inverness in midweek.
Rangers named an unchanged side from the Old Firm derby while Motherwell made three changes from the side who staged their remarkable comeback at Hearts, with Steven Hammell, Maurice Ross and Steve Jennings all starting.
Steven Saunders was out with a knee injury, while Shaun Hutchinson and Tom Hateley were named on the bench.
Rangers started brightly and Motherwell goalkeeper Darren Randolph was called into action to block smartly from Lafferty at his near post.
The home side then had the chance to pile on the pressure when Madjid Bougherra tripped Keith Lasley.
Despite claims for a penalty, the foul had taken place just outside the box and Jamie Murphy’s free-kick failed to make it past the Rangers wall.
Rangers were ahead after 17 minutes when Davis provided the pass for Lafferty, who rounded the goalkeeper before sending an angled drive into the back of the net despite the best efforts of Hammell trying to block on the line.
Motherwell could have been back on level terms almost immediately when a Steve Jones effort took a deflection and a full-stretch Allan McGregor only just tipped past his post.
Well were threatening again when Murphy sent Francis Jeffers through on goal but the Rangers goalkeeper came to the rescue again when he raced off his line to block.
Lafferty – already on a booking – then foolishly insisted on firing the ball into the net despite spotting the offside flag but, fortunately for the striker, referee Mike Tumilty opted to take no action.
Hopes of a Motherwell fightback were dealt a blow when Rangers doubled their lead five minutes after the restart. Gregg Wylde delivered a great ball to the feet of Steven Naismith, whose shot was blocked by Randolph but fell kindly for Davis to rifle home the rebound.
Jelavic then saw his shot crash off the crossbar, before having an effort ruled offside after finding the back of the net.
The Croatian striker was finally on the scoresheet after 64 minutes when he met a cross from Sasa Papac at the back post and nodded home from close range.
Rangers were still hungry for goals and claimed their fourth of the day with 75 minutes gone.
Naismith exchanged passes with Jelavic before leaving Randolph with no chance with a ferocious shot from distance.
With the points secure, Rangers handed a debut to Salim Kerkar as he made his long-awaited first appearance for the club with seven minutes to go.
Naismith then put the gloss on the win with seconds to go as he crashed a fierce swerving shot into the top corner from a tight angle to complete the rout and claim his double.