The Merseysiders have a 100% record in the league and currently sit second after some impressive displays which has seen them score 11 goals, conceding none, as well as an FA Cup win over Chelsea.
And Everton lived up to their early season form by defending resolutely and restricting City to two early chances for former Toffees player Chloe Kelly which were well saved by Tinja-Riikka Korpela.
And on 20 minutes after City had all the play they fell behind to a quick break which ended with skipper Danielle Turner scoring from close range after the hosts failed to clear their lines.
City, meanwhile, have had a slow start by their standards with two wins and one draw in the league and an FA Cup semi-final success which will bring Everton and the hosts together in the final at Wembley on November 1st.
The home continued to dominate the first half but struggled to create clear cut chances as Everton defended in depth and frustrate their opponents.
But an early second half corner restored parity for City as the hard driven delivery by Alex Greenwood was skilfully flicked home by US international Rose Lavelle and her first goal for the club.
Then with 14 minutes remaining City took the lead when Georgia Stanway's driven cross was met with a powerful shot from Kelly.
By now the Merseysiders had used their five substitutes and with it some of their rhythm a fact City took full advantage of and deep into added time Jess Park made it three with a finish from an acute angle.
Man City 3 (Lavelle 52, Kelly 77, Park 90)
Everton: 1 (Turner 20
Venue: Academy Stadium