Doubles from Kenny Miller and Kyle Lafferty, and further strikes from Kris Boyd and DaMarcus Beasley, secured all three points on what was a dazzling afternoon.
Despite the arctic conditions as the teams warmed up the weather improved for kick-off and Rangers took full advantage with a blistering start.
From Craig Thomson’s first whistle they pushed forward with intent and immediately put pressure on the visitor’s fragile backline.
After only five minutes the first goal was scored and it was a belter from Miller.
Davis looked menacing as he moved in to the last third but when he teed up his teammate John Ruddy was helpless as the striker’s curling right foot shot clipped the junction between bar and post before bouncing in to the roof of the net.
It was a superb finish from the Scotland star for his ninth goal of the season; his tenth was not far away.
Despite scoring another early goal Rangers looked hungry for more and only two minutes later Boyd was guilty of missing a great chance.
The prolific no. 9 found space in the box and his right foot shot beat Ruddy but was blocked by a defender.
The ball rebounded back to him but his second attempt was also scrambled off the goal line.
On 13 minutes Sasa Papac decided to wander forward from his left-back slot and the Motherwell defence decided against marking him.
It almost proved costly as Miller dropped deep to receive the ball and his delightful cross found the Bosnian but his glancing header lacked conviction.
Indeed, as he returned to his normal position Ally McCoist could clearly be seen asking the defender why he did not control the ball on his chest before shooting goalward as he was given the time and space to do it.
Nevertheless it was one-way traffic in the opening 20 minutes and Beasley got in on the act when he linked up well with Davis on the right but his left-foot effort from 20 yards was straight at the ‘Well keeper.
The Light Blues were in the ascendancy but their progress was halted when Kevin Thomson sat on the turf nursing what appeared to be a calf injury.
What happened to the midfielder was unclear but he was in a lot of discomfort and he shook his head in frustration as he walked tentatively from the pitch to be replaced by McCulloch.
After such a positive start the only surprise was that Rangers had not scored more but, having not doubled their advantage, Motherwell started to edge back in to the game.
And on 31 minutes a deflected long range effort from midfielder Steven Jennings had Allan McGregor darting across his goal line to make a fingertip stop.
Rangers continue to push forward at every given opportunity before the interval but a dipping free-kick from Steven Davis and a near post shot from Papac which was well saved by Ruddy was as close as they came to doubling their advantage.
The second-half again started positively for the home side they were rewarded for their efforts with another excellent goal with 51 minutes on the clock.
Beasley, who was once again superb, played a delightful pass down the right wing for Steven Davis.
The classy Northern Ireland international only looked up once before swerving a brilliant low cross to the on rushing Boyd who stuck out his right foot boot and diverted the ball in to the net.
The second goal gave Rangers a cushion and it was not long before a third arrived again courtesy of the energetic Miller.
Madjid Bougherra this time played a raking 30-yard pass which sent Miller running through on goal.
For a split second it looked as though the ball was going to skid off the slippery surface through to Ruddy but razor sharp Kenny nipped in at the last second and having rounded the keeper he gleefully found the net from a tight angle in front of the Copland Road Stand.
With three vital points looking to have been secured and Motherwell not at the races it was a shock to the system when they pulled a goal back with 23 minutes remaining.
Shaun Hutchinson bulleted a powerful header past McGregor from an inswinging corner from Tom Hateley.
This however, was only a blip in an otherwise terrific performance and having replaced Kris Boyd on 70 minutes, Kyle Lafferty bagged his side’s fourth on 74 minutes.
Miller was given time and space to turn in the 18-yard box and he slipped a great pass through to the overlapping Broadfoot.
The right-back could have shot himself but he unselfishly played it across goal to Lafferty who stroked the ball in to the empty net from three yards.
After that the flood gates opened with Rangers now toying with their bewlidered opponents.
With less that five minutes remaining Miller found Beasley darting down the right wing and the American advanced goalwards before slotting the ball under Ruddy at his near post.
And with the final whistle about to blow Lafferty latched on to a long pass from the American winger and he nudged the ball past the keeper for his second of the game.
On a day where Rangers had to produce the goods they did so with a stylish display and Motherwell can count themselves lucky it was only six.
Man of the Match – Steven Davis got the award from the home support and deservedly so but DaMarcus Beasley and Kenny Miller were also superb.