An injury-time winner from Hibernian's Kirsty Morrison saw the visitors claim a 1-0 win as our 500th SWPL game ended in defeat at Petershill Park.
There had been little to split the two sides up until the end of the match when City were applying plenty of pressure, but it was our opponents who found the back of the net in dramatic fashion.
One change was made from last weekend's win in the Scottish Cup with Mairead Fulton introduced in place of Natalia Wrobel.
During the opening stages, the visitors saw an early effort from Eilidh Adams whistle past the post but it was the Original Trailblazers who fashioned the best opportunity with some great football seeing Emily Whelan thread Lisa Evans through on goal, with the latter seeing her strike saved by Hibs goalkeeper Noa Schumacher.
The City duo linked up once again to create another chance. A Whelan pass found Evans, and our No.17 cut the ball back to Aleigh Gambone who fired her strike straight at the goalkeeper.
With 28 minutes on the clock, City thought the opener had arrived when Brenna Lovera connected with a free-kick sent into the box. Her effort came back off the inside of the post, but even it had crossed the line, it wouldn't have counted as the American was flagged offside.
And with seven minutes left to go in the first half, Lovera had another opportunity to put us ahead. Whelan sent an inviting cross into the box, which she met with her head and saw it drop just wide of the post.
Those proved to be our best chances of the first half as there was nothing to separate the two sides as it remained goalless going into the interval.
The second half started with City dominating the ball, but with little to show for it in the way of chances created.
Hibs looked to threaten when they won corners in quick succession, but City would hold their nerve and cleared their lines before any danger was capitalised on.
Our best chance of the second half came with 15 minutes left to go when Nicole Kozlova unleashed a drive on the edge of the area that was met by a diving Schumacher in the Hibernian goal.
It was all City in the dying minutes, but it would be Hibs who netted the winner in injury time with Morrison scrambling it home with the last kick of the ball following a corner.
Leanne Ross and her side will be looking to bounce back when we return to SWPL action against Celtic on Friday 28th March at New Douglas Park.
Full-time: Glasgow City 0-1 Hibernian
Glasgow City: Gibson; Warrington, Lauder (Motlhalo), Fulton, Lovera, Whelan (Forrest), Gambone (Wrobel), Evans, Smit, Kozlova (Maatta), van Diemen
Subs not used: Easdon, Walsh, Love, Lockwood, Anderson
Hibernian goals: Morrison 90+7