A sweetly-struck shot from Rachel McLauchlan ensured Rangers kept the title pressure on Celtic - and ended Glasgow City's slim hopes of retaining their SWPL crown.
The win guarantees Champions League football for the Old Firm next season and they go into penultimate round of fixtures in midweek still level on points, with leaders Celtic boasting a 15-goal advantage.
With Celtic having beaten Partick Thistle earlier on Sunday, Rangers knew they could not afford a slip-up at Petershill Park.
But the visitors were on the back foot for much of the first half. Carlee Giamonna's rocket just after the quarter-hour mark richocheted off the underside of the crossbar and somehow failed to cross the line.
City were left cursing their luck again 20 minutes later, as Emily Whelan's ball into the box was almost turned into her own net by Rangers defender Kathy Hill, only for Vic Esson to scramble a desperate save.
And that bad luck came back to haunt the hosts just before the half-time whistle.
McLauchlan collected a cheeky backheel from Kirsty Howat on the edge of the penalty box - and her shot curved past Lee Gibson high into the opposite corner.
City pressed for an equaliser - Giamonna's volley forcing another top-notch save from Esson - and had a good shout for a penalty after turned down after Mia McAuley appeared to block a free-kick with her arm.
Rangers occasionally threatened on the break, with McAuley and Sarah Ewans both forcing saves from Lee Gibson, but it was the at the other end of the pitch where the pressure largely lay, and where Esson's heroics kept alive Rangers' title challenge.