Chantelle Swaby opened the scoring for Gers in the second-half, before City responded quickly through Niamh Farrelly.
Malky Thomson named just one change to his side from last weekend’s 8-0 victory over Aberdeen, as striker Jane Ross returned to the starting XI with Kayla McCoy on the bench.
The Light Blues had a fantastic chance to open the scoring in the first five minutes of the match, Kirsten Reilly picked out Chelsea Cornet just inches from goal but her effort was blocked well by Alexander before the hosts managed to clear the danger.
It was a fairly even opening 15 minutes at Petershill Park as both sides looked to make the breakthrough early on in the match.
Jo Love was booked for a challenge on Kirsten Reilly at the half-way line, but the Glasgow City midfielder picked up a sore one and had to be replaced by Mairhead Fulton with just 17 minutes played.
On the half-hour mark, Glasgow City had a chance from a set-piece which Hayley Lauder curled towards goal but it was held comfortably by Jenna Fife. In another free-kick for the home side shortly after, Pricilla Chinchilla drilled a low shot as she tried to beat Jenna Fife at the near post but it was held by the Rangers goalkeeper.
With just over five minutes remaining before the break, Jane Ross saw a shot held by Lee Alexander, before Lizzie Arnot saw a shot deflected wide.
In a lively start to the second-half, Hayley Lauder had a left-footed shot saved by Jenna Fife before Jane Ross delivered a dangerous ball across the face of goal at the other end which City managed to clear from the path of Lizzie Arnot.
It was Rangers that got the breakthrough with 55 minutes on the clock. A corner was whipped into the box by Lizzie Arnot and met the head of Chantelle Swaby. The defender showed strength to get the ball on target and despite goalkeeper Lee Alexander getting a touch, she couldn’t stop the ball landing in the back of the net as the visitors took the lead.
However, that advantage lasted just over five minute as the hosts drew level. A ball was swung into the box by Megan Foley and Niamh Farrelly got on the end of it to oop a header over Jenna Fife.
Rangers thought they had taken the lead again with 67 minutes on the clock as Rachel McLauchlan delivered a ball across the face of goal which was tapped in by Lizzie Arnot but the flag was up for offside.
Lauren Davidson forced another save from Jenna Fife shortly after as she went on a solo run down the left before getting a low shot away at goal.
Mairead Fulton tried an effort from distance in the final few minutes of the game as she drilled a shot towards goal but it drifted just wide of Jenna Fife’s left-hand post.
In injury time, the ball broke for Demi Vance at the edge of the box and her shot was blocked before the rebound fell to Jane Ross but Lee Alexander blocked the effort from close range to see the game end level.
RANGERS: Fife, Docherty, Vance, Middag, Hay (McCoy, 63), Reilly, McLauchlan, Ross, Arnot, Cornet (Westrup, 79), Swaby.
Subs: Cunningham, Ness, Maclean, McLeary, Watson.
Glasgow City: Alexander, Davidson, Lauder, Walsh, Love (Fulton, 17), Clark, Farrelly, Colvill (Fulutudilu, 66), Molin, Chinchilla, Foley.
Subs: Clachers, Michie, Pimenta, Dodds, Noble.
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