The success keeps Gers’ excellent start to the domestic campaign going and this was their fifth win in six league games.
It also extended the team’s unbeaten run at Ibrox to 21 games in all competitions, with the last loss there coming against Lyon last December.
Walter Smith sprung a surprise when he named his team by dropping Allan McGregor, who was at fault for Kilmarnock’s goal last week, to the bench.
Neil Alexander started in the regular keeper’s place, with Kevin Thomson and Christian Dailly also coming into the team
On a bright afternoon, Rangers started well and Kenny Miller had the first opportunity of the game with less than three minutes gone.
Madjid Bougherra took a quick free kick to Davis and when he lifted the ball forward to the Scotland striker, he shot just over from the edge of the box.
Pedro Mendes was at the heart of most good things Gers did in the opening stages and his vision stretched a Motherwell team without a win at Ibrox in 20 visits.
Without creating too many clear-cut chances, the hosts were dominating and it seemed only a matter of time before they would break the deadlock if they could hit the target.
But play then began to break up a little, passing by both teams became disjointed and the match lost its rhythm to an extent.
The Light Blues almost gave away a careless opener too, with Alexander kicking straight into Chris Porter and the ball spinning back towards goal but past the post.
That sparked a reaction from the crowd, as did a shocking late challenge by Paul Quinn on Mendes which earned him a yellow card.
Well, in fact, were guilty of several mistimed tackles and that led to an animated touchline debate between Rangers manager Smith and referee Eddie Smith.
When another lunge brought Stephen Craigan a caution for pulling down Miller, David Weir also went into the book for the ferocity of his protests and temperatures rose further.
Finally play improved again and a good move by Gers ended with away keeper Graeme Smith tipping a low curler from Miller past when it was sneaking in.
Davis also had a go but his drive after some enterprising play by Kirk Broadfoot was always swerving away from the upright.
It seemed Miller had stroked in to break the deadlock at last when Kris Boyd set him up and some good footwork fooled the Motherwell defence.
But the ball run inches wide and a tetchy first half came to a close with the scoresheet still blank.
The home side continued to press after the restart and DaMarcus Beasley, who had a poor afternoon, saw his effort stopped by Smith.
Boyd then cracked the post with a great shot on the turn after he was set up by the impressive Davis.
Frustration was starting to creep in as Mark McGhee’s visitors’ gameplan was limiting what Rangers could do.
But then, just as it seemed it might take a substitution to change the course of the game, the Light Blues went in front.
Miller, who had a good match, played to Boyd and with a cute flick, he released Davis and the Northern Ireland midfielder slotted home from 15 yards.
It was his first goal for the club since he signed a permanent deal from former club Fulham and the strike was a popular one.
Armed with an advantage, Smith’s men set about trying to extend it and some great interplay between Miller and Boyd almost led to a second.
But when the latter simply fell over in the penalty area, he was given a ridiculous yellow card by the referee for an alleged dive.
Back came the Steelmen, who would have levelled through David Clarkson had it not been for Alexander’s excellent fingertip save.
Despite their midweek European exertions, Motherwell were finding a second wind and that rattled Rangers.
Clarkson had another go but his clip flashed wide and it was another big let off for the Ibrox outfit.
Novo came on for Beasley and tried to lift the pace, surging past one player but then sending the ball into the side netting.
He was more successful with 15 minutes remaining as he made the points safe with his first goal of the season.
Miller was his supplier, sending in a teasing cross after Davis released him and the Spaniard bundled in from close range.
Porter should have pulled one back late on but miskicked and hit the post while Boyd sent Miller clear and the forward pulled wide when he might have done better.
Clarkson did then net as he converted from six yards but the goal was nothing more than a consolation in the end and Rangers continue to set the pace in the title race.