The home side controlled proceedings for long periods without finding a breakthrough until Stott headed home to put her side in the lead in the with less than 20 minutes left to play.
City had the majority of chances during the clash with Alanna Kennedy's curling free-kick one of their better opportunities.
The introduction of Rhali Dobson from the bench proved to be an inspired decision for City coach Patrick Kisnorbo as she fired an inch-perfect pass to Stott to put into the back of the net.
Melbourne Victory keeper Casey Dumont made an acrobatic save to deny City's Jess Fishlock from scoring an incredible long range strike.
Victory had a late chance to equalise but Laura Alleway's header was cleared off the line by City to secure the win and all three points.