Hearts dropped from first to fourth after Glasgow City managed to nab all three points late on at their temporary home of K-Park.
Amy Muir opened the scoring for City but there was drama at the end of the first half as Kimberley Smit was shown a red card and gave away a penalty.
Hearts' Lisa Robertson converted from the spot but new signing Sofia Maatta stepped up with five minutes left on the clock to make it 2-1.