Haley Rosen's first half goal against Spartans was enough to maintain Glasgow City's lead at the top of the SWPL.
Closest challengers Hibernian Ladies ran out 5-0 winners against Stirling University, with the match played at Easter Road ahead of their up coming Champions League clash with Bayern Munich.
Elsewhere, Celtic came from behind to beat Rangers 3-1.
And Aberdeen were 1-0 winners at home to Forfar Farmington.
Glasgow City head coach Scott Booth was frustrated despite the 1-0 win.
"We created so many chances and should have been far more clinical in taking some of them," said Booth.
"That said, it is another three points and with only four games left in the title race, another vital three points to keep us clear at the top of the table."