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Wilma Forsblom scored in injury time to wrap up the victory for City.
Glasgow City continue to set the pace in the SWPL after a derby victory over Partick Thistle on a day the top five clubs all won.
American forward Brenna Lovera was the star of table-topping City's win at Petershill Park, opening the scoring then netting a penalty in the second half.
Wilma Forsblom wrapped up the win in injury time to keep City a point clear.