The Jambos were deserved winners at the Balmoral Stadium and could have left the Granite City with a more handsome victory but were twice denied by the woodwork in the second half.
Eva Olid's side remain ninth in SWPL 1 but are now level on points with Partick Thistle and just a point adrift of seventh-placed Motherwell.
Elsewhere, it was a sorry afternoon for both Hibernian Women and Spartans who went down 5-0 and 4-0 to Rangers and Glasgow City respectively.
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Dean Gibson's Hibs remain fourth with Spartans eight points worse off in sixth.
Meanwhile, Boroughmuir Thistle's top-flight promotion hopes were boosted by an emphatic 5-1 victory over Kilmarnock at Rugby Park.
Samantha Duncan scored twice, with Anna Murray, Beth McLeod and Fiona Gibson also on target.
Suzy Shepherd's side are currently second in SWPL 2, a point better off than Glasgow Girls, and will join champions Dundee United in SWPL 1 next season if they finish runners-up.