Lizzie Arnot’s second-half goal secured all three points at Rangers Training Centre.
Malky Thomson named one change to his side from last weekend’s 5-0 victory over Spartans with the injured Zoe Ness being ruled out of the matchday squad and Brogan Hay coming into the starting XI.
Jenna Fife was in goal for Rangers with a back four of Nicola Docherty, Brianna Westrup, Chantelle Swaby and Rachel McLauchlan.
Kirsten Reilly, Emma Brownlie and Sam Kerr made up the midfield, with Brogan Hay and Lizzie Arnot supporting Kirsty Howat in attack.
The visitors were forced into a change before the match as Amy Gallacher picked up an injury in the warm-up and was replaced in the starting XI by Ria McCafferty.
Rangers first tested Emily Mutch in the 10th minute as they were awarded a free-kick on the edge of the box. Lizzie Arnot curled a left-footed effort towards goal which was held at the second attempt by the goalkeeper.
Arnot came close again shortly after following some good build-up play from Rangers. A one-two down the left-hand side between Nicola Docherty and Emma Brownlie saw them pick out Arnot on the edge of the box and she took a lovely touch before getting a shot away but it was just wide of the target.
Play was stopped around the 26th minute as Rangers captain Brianna Westrup and Shannon Leishman clashed heads in the box, both players were fit to continue after receiving treatment.
Gers threatened again from an Emma Brownlie corner as Chantelle Swaby’s header forced a save from Emily Much as the Hibs number one pushed the effort wide of the target.
Rangers continued to push for a breakthrough before half-time as Nicola Docherty saw an shot from distance held by the keeper before Kirsten Reilly also saw a shot saved by Emily Mutch leaving the game goalless at the break.
However, it only took Rangers two minutes into the second-half to get the opening goal. Sam Kerr fed the ball through to Brogan Hay down the right with the winger picking out Lizzie Arnot who lifted the ball high into the back of the net for her ninth goal of the season.
As Rangers looked for a second, Rachel McLauchlan’s shot was blocked by Hibs to deny the Rangers right-back.
Sam Kerr almost doubled the advantage late in the game as the ball broke to her in the box but her shot bounced back off the crossbar.
RANGERS: Fife, Docherty, Brownlie (Gemmell, 71), Hay (Bourma, 80), Reilly, McLauchlan, Arnot, Howat (Devi, 87), Kerr, Westrup, Swaby.
SUBS: M. Cunningham, Girasoli, Cornet, H. Cunningham.
HIBS: Mutch, Boyle, Murray, Eddie, Leishman, Notley, Morrison, Muir, McCafferty (Boyce,64), Cavanagh (Handley, 78), Adams.
SUBS: Donald.