Goals from Jill Scott, Toni Duggan and a Lindsay Johnson own goal proved enough for the victory, condemning the Toffees to a third straight defeat to the Mancunian outfit this season.
With his side still on a high after booking their place in the Continental Cup final, manager Nick Cushing made just two changes from the team who secured a hard-earned win over Chelsea Ladies last time out.
Alongside captain Steph Houghton and Abbie McManus, Chelsea Nightingale and youngster Georgia Brougham were thrust into the defensive back-line in place of Emma Lipman and Paula Radtke.
Betsy Hassett, Isobel Christiansen and Scott operated in midfield, while Duggan, Krystle Johnston and Natasha Flint took their positions in more advanced roles.
It took just six minutes for the visitors to take the lead. Johnston - a thorn in the hosts' side all afternoon - delivered the perfect cross for Scott to slot home, against her former club.
Everton responded well to falling behind though and Karen Bardsley was called into action on a number of occasions to preserve City's lead.
The England shot-stopper saved well from Michelle Hinnigan and Alex Greenwood, before Brooke Chaplen volleyed wide.
Having survived that period of pressure, the visitors settled and began to take control of the game.
In search of some much-needed breathing space, Cushing's side rallied for a second goal. Houghton tried her luck with a free-kick that flew just over the bar, after Duggan had been upended on the edge of the area from Hassett's through-ball.
Despite dominating possession for much of the first half, the away side couldn't extend their advantage and headed into the break as deserved leaders.
After the restart, City continued where they left off and they did double their advantage on 56 minutes. Christiansen, who celebrated her 23rd birthday yesterday, drilled in a dangerous cross which caused Johnson to turn the ball into her own net.
With a comfortable lead against a side bottom of the FA Women's Super League, the visitors sought to increase it. Johnston forced Megan Walsh into a fine save with a powerful effort that was tipped over.
Christiansen and Duggan were particularly impressive and caused the hosts problems all afternoon. The latter capped her performance with a goal in the dying seconds to seal an excellent win.
The former Toffee latched onto a pinpoint Flint pass before smashing the ball into the back of the net, continuing her fine scoring run.
Next up for City is a trip to Bristol Academy on Sunday 28 September. The Mancunian outfit will look to end the season strongly in preparation for October's cup final clash with Arsenal Ladies.
There is only one way to watch City’s Capital One Cup third round clash with Sheffield Wednesday live.
The first step towards defending our trophy won at Wembley in March will not be shown live on TV anywhere in the UK, so make sure you’re at the Etihad Stadium on Wednesday 24 September.
Prices start at £5 for under-16s and £15 for adults, so no excuses: get your ticket now and make sure you don’t miss out!