It was a thoroughly deserved triumph for the Light Blues as they continue their pursuit of further silverware this term, earned through goals from Rio Hardy from the spot, a stunning strike from Lizzie Arnot, Chelsea Cornet, and substitute Mia McAulay.
And with a trip to the capital to face Hearts in midweek, as well as a clash against Partick Thistle in seven days’ time, the victory was exactly what the doctor ordered ahead of a crucial three-game week for the side.
There was a spring in Rangers’ step straight from the off, encapsulated inside six minutes when Rachel Rowe burst forward from midfield and unleashed a powerful drive that sailed straight down the throat of Lee Gibson.
It was one-way traffic in the direction of the Glasgow City goal, with a sweeping move involving Rio Hardy and Jane Ross almost engineering an opener for Lizzie Arnot when she looked to latch onto Ross’ dangerous delivery across goal.
Kathy Hill was next to test her luck as she met Rowe’s floated free-kick at the far post, but she could only guide her header into the grateful hands of Gibson.
Such was Rangers’ dominance in the early exchanges that it was only a matter of time before the opening goal arrived, duly coming via the penalty spot moments later.
Kinga Kozak was the guilty party in City colours as the midfielder was adjudged to have brought down Rowe with Welsh international advancing into the penalty area. From 12 yards out, Hardy assumed spot-kick responsibilities and, like she did in the reverse fixture back in November, she dispatched with aplomb to give Rangers the lead.
Potter’s side had their tails up following the breakthrough and they were almost rewarded with a second goal three minutes later. An intricate move through the heart of the Glasgow City midfield allowed Chelsea Cornet to feed a pass into Hardy with her back to goal; Rowe was positioned perfectly at the edge of the penalty area before her goalbound effort deflected inches wide.
Against the run of play, however, the visitors restored parity. In a rare moment where City were able to receive in midfield and pick their heads up, a clever run from Scotland international Lauren Davidson allowed the attacker to steal a march and stab a cute finish beyond Jenna Fife.
Rangers ought to have produced an immediate21 riposte with five minutes remaining before the interval. Again, it was one-touch play which cut the away side open, allowing Rowe to hit the byline and lift a delightful pass into goalscorer Hardy who nodded wide from close range with the goal at her mercy.
Another headed opportunity went begging for the forward just seconds after the restart as she leapt impressively from Brogan Hay’s delivery but nodded off target.
The away side then reminded Rangers of their threat on 52 minutes when Davidson collected possession in a dangerous area on the edge of the penalty area, although her resulting effort didn’t trouble Fife between the posts.
And the warning sign only served to sharpen the Gers’ focus as they restored their advantage in spectacular fashion less than 60 seconds later.
Space opened up on the left-hand side for the hosts as possession found its way to Arnot. The 28-year-old took the ball in her stride and advanced towards goal, shifting the ball onto her favoured right foot before sending an unstoppable effort into the far top corner which left Gibson with no chance in the City goal.
The next goal, as a result, would be priceless, with Rangers going in search of the decisive strike when substitute Mia McAulay robbed City of possession in midfield. Lifting her head, she fed a delightful pass into Kirsty Howat whose lay-off ricocheted off Kenzie Weir and trundled out for a corner.
Conditions at Broadwood – with the wind swirling around the three stands - certainly weren’t conducive to free-flowing football, but there was still a doggedness about Rangers as they chased the all-important third goal to kill the contest.
The opportunity appeared to be falling to Hardy with nine minutes remaining as she dovetailed nicely with Howat, but City recovered quickly to concede the corner.
However, from the resulting set-piece the deserved third goal arrived for Potter’s side. Indeed, Chelsea Cornet didn’t appear to know too much about it as the ball cannoned off the midfielder and into the bottom corner to seal all three points for the home side.
And there was still time for the Light Blues to embellish their performance as McAulay fired home a fourth goal of the contest, skipping inside and guiding a delightful finish into the far corner.
RANGERS: Fife, Docherty, Hill, Middag, Hay, Rowe (McLeary, 85), Hardy (Rowe, 85), Ross (Howat, 57), Arnot (McAulay, 57), Cornet, McLoughlin (Bance, 90)
Subs not used: Esson, Austin, Martinez
GLASGOW CITY: Gibson, Muir, Lauder (Wardlaw, 60), Fulton, Whelan, Davidson (Colvill, 75), Kozak (Gambone, 75), Moore, Weir, Oskarsson, Brown (Forrest, 9)
Subs not used: Easdon, Warrington, Walsh, Love, Forsblom