Nick Cushing’s side started slowly on Merseyside but goals from Tessa Wullaert, Lauren Hemp and two from Gemma Bonner made it a comfortable victory.
The Toffees had levelled through Molly Pike’s sensational strike, but City dominated the second half and added goals which could prove vital in our bid to qualify for the quarter-finals of the competition.
We’ll have to wait until the final round of group fixtures, when Manchester United face Birmingham City before we discover our fate, but this performance and result which puts us in a strong position.
Everton came into the game without a win in the competition but victory over rivals Liverpool in their previous game appeared to have a galvanising effect.
They started strongly and their slick passing and pace across the front-line opened City up on several occasions.
Hannah Cain fired wide when she should have done better, before Ellie Roebuck had to be alert to thwart Elise Hughes after Pike’s cute through ball unlocked the visitor’s defence.
They were half chances, but it was chances Cushing’s side were struggling to create and the vociferous travelling City contingent breathed a sigh of relief when FA WSL top scorer Chloe Kelly’s half-volley clipped the top of Roebuck’s crossbar.
City, who were forced into an early change when Megan Campbell limped off, responded, however and started to play the game in the host’s half.
Ellen White sent a speculative header wide of Kirstie Levell’s post, before the ‘keeper came sprinting off her line as White tried to latch onto Caroline Weir’s slide rule pass and then City struck.
Bonner lost her marker in the six-yard box and glanced a header in off the post from a Wullaert corner for a first goal that looked like it might be crucial in what was proving to be a tight contest.
City were much improved in the second half, but only after being rocked by a 20-yard thunderbolt from Pike immediately after half-time.
Roebuck had no chance and it was the sort of goal which could have spurred the hosts on, but the reigning champions responded instantly to retake the lead within four minutes.
Wullaert, who was particularly impressive after the break, showed great composure to prod home at the far post after the Toffees failed to deal with a right-wing cross and from there, we never looked back.
Jill Scott might have scored but for White, who inadvertently got in the way of her team-mate’s effort to divert the ball wide after good wing play from Demi Stokes.
It was the free-flowing play we expect from City and another goal looked likely, but in testing conditions on Merseyside we were not averse to taking a more direct approach.
And we reaped our rewards when Steph Houghton powered Wullaert’s corner back across goal for Bonner to fire emphatically into the roof of the net.
Having put five past West Ham at the weekend, Cushing had called for a similarly clinical display and his side certainly met his request.
Time and time again Stokes, Janine Beckie and Hemp got to the byline and peppered the Everton area with crosses and the latter eventually got her reward as she dribbled across the area before firing past Levell to seal a hard fought and well deserved win.
City had more to celebrate, too, with Laura Coombs making a cameo appearance from the substitute bench, her first since a knee injury ruled her out at the end of September.
Roebuck's goal was protected by a back four of Beckie, Houghton, Bonner and Campbell.
Walsh, Weir, Hemp and Scott formed the midfield quartet with Wullaert and and White playing in tandem up front.
What it means
With three wins and a draw we are the first club to complete our Group C fixtures, but other teams’ games in hand mean we don’t yet know whether we have qualified for the quarter-final stage.
We are level on nine points with Manchester United, who top the group on goal difference and have one game remaining against third-placed Birmingham City, which will determine our fate.
Should United win or draw that game, we will qualify for the last eight in second place, but if the West Midlands can win by four goals, they would claim the second qualifying spot.
FA WSL action returns on Sunday, when we travel to winless Bristol City for a 12.30pm kick-off at Stoke Gifford Stadium.
Should we reach the last eight of the Continental Cup, the draw for that stage will take place in the days following the final group stage fixtures on Wednesday 11 December, with the quarter-final ties scheduled for Wednesday 15 January.