Jodi McLeary continued her scintillating form with the only strike of the contest as she stroked home from Eva Hendle's cut-back midway inside the first-half.
It means the Gers remain at the summit of the division heading into the forthcoming international break.
From the team which squared off against Hammarby IF in midweek, there were as many as seven changes to the starting lineup.
One of those, Hendle, looked menacing in the opening exchanges when she danced down the left and drew a corner on the byline.
From the subsequent delivery, Katie Wilkinson drifted into space at the far post but was penalised for a handball as she looked to scramble over the goalline.
The forward turned creator moments later to free Bailley Collins down the right, and after weaving her way beyond her marker her initial effort was blocked before the hosts were able to recover any bodies to alleviate the danger.
Such was the blustery conditions in the north of Glasgow that an attempted delivery by Collins advanced on the right almost sailed into the near top corner but for an alert intervention by Ava Easdon between the posts.
The action subsided for a prolonged period before Hay was freed down the right with white jerseys bursting into the penalty area, but her delivery flashed across goal and out for safety.
However, there was no denying the Gers just three minutes later as they broke the deadlock in fine fashion.
Collins showed tremendous persistence through the heart of the pitch to find Hendle on the left whose pull-back to the edge of the penalty area was pinpoint into the path of McLeary who stroked a first-time finish into the bottom corner on her unfavoured left side.
One could have become two very quickly when Wilkinson, not for the first time, released Hendle beyond the Thistle backline. With just the goalkeeper to beat, she elected to round Easdon, but the on-loan Chelsea youngster was denied by a cluster of Thistle bodies haring back to clear the danger.
The home side had offered very little but briefly threatened before the interval when a deep free-kick delivery was cleared only as far as Rachel Donaldson who volleyed wide.
As the second half began, the Gers sought a cushion to their advantage as Sophie Black dug out an effort from the edge of the penalty box after being teed up by Wilkinson, but her strike was of the stabbed variety and was comfortably collected by Easdon.
The visitors cut through Thistle once again on the hour-mark when Wilkinson laid a delightful pass into the path of Black who strode onto the ball perfectly but planted her strike from distance just wide of the post.
Wilkinson blasted over from just inside the penalty area before nodding wide from a Calliste Brookshire delivery.
Although the scoreline remained in the balance, the home side never truly threatened Jenna Fife's goal as the Gers saw out the three points in Petershill.
RANGERS: Fife, Collins (Roelfsema, 66), Austin, Boyce, Docherty, Thrysoe (Blake, 75), Black (Cruft, 60), McLeary (Smith, 90), Hay (Brookshire, 60), Hendle (Berry, 66), Wilkinson
Subs not used: Rarity, Hill, Connolly-Jackson
PARTICK THISTLE: Easdon, Falconer, Love (McKenna, 11), Robinson, Donaldson (Henderson, 63), Bulloch (Syrjanen, 76), Timlin (Ferguson, 76), Longcake, Dawson (Cowan, 76), McGoldrick, Hay (Slater, 63)
Subs not used: Logan
