After enjoying the better of the opening period, the Gers were pegged back shortly after the interval when Lisa Martinez was penalised for a dubious foul on Emily Whelan, with Lauren Davidson converting from the penalty spot.
However, the Light Blues found the leveller from 12 yards themselves, as Tessel Middag dispatched with aplomb after Kayla McCoy went down under contact from a throw-in.
Malky Thomson named one change to his Rangers side for the short trip across the city, with Maddie Nolf replacing Nicola Docherty in defence.
It took just a few short minutes for the Light Blues to engineer their first opportunity of the contest. Jenny Danielsson floated a gorgeous cross towards Brogan Hay at the far post whose control proved immaculate, drawing a fine diving stop from the Glasgow City goalkeeper with her resulting effort.
Mairead Fulton flashed inches wide of Victoria Esson’s post minutes later for the hosts, lashing an effort from the edge of the penalty area after the ball had fell invitingly from a corner.
Lauren Davidson headed wide for the home side as both teams enjoyed their spells of superiority, with the Light Blues looking particularly dangerous down the right-hand side.
Thomson’s side threatened on 22 minutes as Tessel Middag arrowed a left-footed effort from the edge of the penalty area, but Megan Foley was on hand to block the 29-year-old’s goalbound strike.
Sam Kerr showed tremendous energy from the front to steal possession in the 29th minute before driving towards goal, but the Scotland international could only send her effort straight into the arms of the Glasgow City goalkeeper.
Rangers were beginning to build a head of steam and, just minutes later, Kayla McCoy almost capped off a well-worked move, with Nolf’s pull-back cleared to safety before it could reach the lurking Gers forward.
Glasgow City were throwing their bodies on the line to deny Rangers towards the end of the opening period. Hay showed her quick feet on the right before sending a cross towards Kerr inside the penalty area, with a heroic block denying the midfielder’s goalbound effort from 15 yards out.
Chelsea Cornet then sent a speculative effort inches over the crossbar, before the Light Blues manufactured their best chance of the first half.Lisa Martinez rose highest from a dangerous corner, heading agonisingly over from inside the six-yard box while under pressure from several Glasgow City defenders.
Rangers picked up where they left off before the half-time whistle, with McCoy quickly threatening down the left as she looked for Hay inside the penalty area.
However, the Light Blues suffered a setback just six minutes into the restart. Emily Whelan latched onto a pass down the inside right before falling under apparent contact from Martinez as the two crossed paths, with the referee pointing to the penalty spot after a brief delay.
Davidson made no mistake from the penalty spot for Glasgow City to break the deadlock, planting her penalty into the bottom corner and sending Esson the wrong way.
An injury to Priscilla Chinchilla for the home side slowed the pace of the game down as Rangers went in search of a response.The Light Blues’ patience told, however, as they found the equaliser in the 70th minute.
McCoy went down as she spun in the penalty area from a Rachel McLauchlan throw-in, with the referee pointing to the penalty spot for the second time in the match.
Middag showed nerves of steel to claim the ball, dispatching her spot-kick into the left-hand corner to draw her side level.
Emma Watson replaced Jenny Danielsson with seven minutes remaining as the Light Blues looked to complete the turnaround and claim a priceless three points.
There was late goalmouth action as substitute Lizzie Arnot centred from the left in search of McCoy, but the ball failed to stick with the forward after Glasgow City cleared desperately to safety.
Rangers were then left with their head in their hands minutes later as the crossbar was rattled from a free-kick. Middag’s floated delivery from the right was met by Martinez, but the defender could only power her header off the upright after timing her leap to perfection.
Thomson’s side were piling on the pressure in the dying stages, with substitute Kirsty Howat flashing a wicked ball across goal that trickled narrowly wide of the far post and out for a corner.
Middag fired towards goal in stoppage time from a Watson pull-back as the winning goal proved elusive for the Gers, keeping their unbeaten start to the league season going.
GLASGOW CITY: Gibson, Muir, Lauder (Prades Insa, 45), Walsh, Fulton, Whelan, Clark, Davidson, Kozak, Chinchilla (Martin, 60), Foley.
Subs not used: Clachers, Warrington, Grant, Gibb, Allie, Noble, Ritchie.
RANGERS: Esson, McLauchlan, Davison, Martinez, Nolf, Cornet, Middag, Hay (Arnot, 73), Kerr, Danielsson (Watson, 83), McCoy (Howat, 86).
Subs not used: Fife, Hill, Maclean, Docherty, Cavanagh, McLeary.