The blues started strongly and opened the scoring within only eight minutes when clever footwork saw Caroline Weir dance through the defence before nonchalantly slotting past Courtney Brosnan.
Everton quickly netted a reply, with Grace Clinton scoring her first-ever goal for the Toffees when she cooly curled the ball into the far post, but that was as close as they would come to gaining a foothold on the game.
City were dominant, particularly on the wings, and Everton resulted to sitting back in an attempt to break down the hosts' play.
And they would be rewarded for their dominance. Bunny Shaw bagged her sixth of the season shortly before the break and then Hemp, Jess Park and Ellen White extended the tally to five in the second half.
The blues will hope that they can carry this form into the league, and coupled with the return of players from the international break, put their poor start to the season behind them.