Laura Berry brought the Gers level before Katie Wilkinson’s stunning strike completed the turnaround after the break.
Leanne Crichton made just one change to the side that defeated Hibernian on Sunday, with Hannah Blake coming into the starting line-up in midfield.
On a wet and windy evening, Rangers and Glasgow City took time to settle into the game, with both sides looking to find their rhythm in the opening stages.
Rangers’ first opportunity saw Laura Berry combine with Jodi McLeary down the right before cutting the ball back into the path of Kirsty Smith, but her effort was comfortably gathered by Lee Gibson.
Glasgow City took the lead when Claire Whelan exchanged a one-two with Amy Muir before driving at Eilidh Austin and cutting inside to get a shot away. Shu Ohba made the initial save, but Kelly Brady was on hand to convert the rebound.
Rangers responded impressively after the break, stepping up the pressure as they looked to turn the game around.
The equaliser came when Austin drove forward down the right and delivered a dangerous low cross into the box. Gibson could only parry the ball into Berry’s path, and the forward made no mistake from close range to bring the Gers level.
With momentum firmly behind them, Rangers continued to put Glasgow City under pressure and completed the turnaround just after the hour mark. Wilkinson spotted Gibson off her line before unleashing a superb strike from distance, finding the bottom corner to send the Gers in front.
A strong second-half display saw Rangers fight back to secure a valuable victory and strengthen their position at the top of the table.
Attention now turns to Sunday, as the Gers return to Broadwood Stadium to face Motherwell.
RANGERS: Ohba, Smith (Collins, 54), Austin, Roelfsema, Docherty, McLeary, Blake (Hay, 54), Cruft, Berry, Wilkinson, Brookshire
Subs not used: Fife, Boyce, Hill, Connolly-Jackson, Black, Ewens
GLASGOW CITY: Gibson, Kotyk, Muir, Forrest, Motlhalo, Whelan, Rossman, Evans, Brady (Seaby, 78), Kurosaki, Gray (Primmer, 82)
Subs not used: Clachers, Lauder, Harrison, Määttä, Lane, Martin