Kathleen McGovern struck the opener for the visitors in the first half, before the Hibs attacker doubled her tally midway into the second period and Rosie Livingstone sealed all three points for the Edinburgh side in the dying embers of the contest.
It was a second successive defeat for the Light Blues, who will welcome the forthcoming winter hiatus in order to reset as a squad and go again in the new year.
To the surprise of most inside Broadwood it was Hibs who were in the ascendancy early in the contest. Tegan Bowie found herself through on goal down the left-hand side with only Vic Esson to beat, although the New Zealand international was equal to her effort from an admittedly acute angle.
The Light Blues failed to heed the early warning as the visitors opened the scoring inside seven minutes.
Indeed, it appeared an innocuous delivery into the Gers penalty area but a mix-up allowed Kathleen McGovern to steal in and lift her finish over a stranded Esson.
The Rangers goalkeeper was then equal to an impressive Kirsten Reilly free-kick which looked destined for the top corner from 25 yards out.
Hibs ought to have doubled their advantage soon after when Stacey Papadopoulos was released beyond the Gers defence but, with only the goalkeeper to beat, her curled finish came back off the inside of the far post much to the relief of the Light Blues faithful.
Charlie Devlin looked most likely to find a route back into the contest for the hosts, drawing a save from Erin Clachers down to the Hibs goalkeeper’s left-hand side.
Rangers slowly began to build momentum as the first half wore on and they were again lamenting Clachers in the away side’s goal when she was down smartly to deny Kirsty Howat’s first-time effort from 15 yards out.
The home side emerged from the interval with a renewed purpose and a dangerous delivery from Arnot was glanced goalwards by Howat but wide of the target.
Jo Potter turned to her substitutes bench just shy of the hour mark as Katie Wilkinson replaced Charlie Devlin.
However, despite Rangers’ control of possession, they were struggling to find a route through a resolute Hibs defensive block.
And with 11 minutes remaining it was the visitors who struck to leave Rangers with a mountain to climb after McGovern’s thunderous effort sailed into the top corner from distance.
Two soon became three for the Edinburgh side as Livingstone sprung the offside trap and, with only Esson to beat, the Hibs substitute poked her finish beyond the New Zealand international to compound a disappointing day for the home side.
RANGERS: Esson, Docherty, Eddie, Hill (Middag, 45), Devlin (Wilkinson, 58), Howat, Hardy (McAulay, 45), Arnot (Hay, 80), Cornet, MacLean, McLeary
Subs not used: Fife, Rafferty, Ross, Austin, Lafaix
HIBERNIAN: Clachers, Hunter, Papadopoulos (Christie, 90), Grant, McAlonie (Taylor, 74), Adams, McGovern (Livingstone, 82), Doran-Barr, Bowie, Reilly, Lawson
Subs not used: Schumacher, Leishman, Ferguson, Boyle, Morrison