An 89th-minute goal for youngster Natasha Flint was enough for the three points, which ensures the Blues are off the mark in Group Two.
Following Thursday night’s narrow defeat away to Doncaster, Nick Cushing's side had little time to prepare for this encounter but relished the chance to bounce back quickly.
Cushing opted to make two changes to the team that lost at the Keepmoat Stadium, with Abbie McManus replacing Steph Marsh and Krystle Johnston playing as the lone striker up front in Toni Duggan’s enforced absence.
City started the brighter of the two teams and almost broke the deadlock after just three minutes. Following a neat one-two between Isobel Christiansen and Betsy Hassett, the former took a touch to compose herself but dragged her shot wide.
Flint then tried her luck with a curling effort but Rachel Brown-Finnis in the Toffees' goal was equal to it.
Everton – content to play on the counter-attack – could only muster two attempts in the first-half, with Nikita Parris proving to be their main threat.
On 11 minutes, the striker’s decision-making cost the visitors as – racing down the left – she chose to ignore the support arriving at the back-post and fired a shot well over the bar. During the build-up, City’s Emma Lipman suffered an injury and had to be replaced by Chelsea Nightingale.
The hosts shaded possession in the opening 45 minutes and created the better chances. Much like in previous games though, it was the clinical finish that evaded the Blues. Hassett’s tame effort was easily scooped up before Johnston fired a shot straight at Brown-Finnis and Scott – set up by the influential Christiansen – attempted a chip which lacked pace.
The second-half produced very little in terms of goalmouth action until the 65th minute. A dangerous cross nearly ended with an Everton defender heading into her own net and from the resulting corner, an almighty scramble in the six-yard box was almost poked home but the Toffees somehow managed to prevent the ball from crossing the line.
That incident sparked the game into life. Flint saw a low shot deflected wide before captain Steph Houghton thought she’d broken the deadlock only for her header to be superbly pushed wide.
Everton then spurned a glorious chance to nick a goal against the run of play. The Toffees opened up the City defence but were too tentative in pulling the trigger. Eventually, when Kelly Jones tried her luck, the shot was straight at Karen Bardsley.
City responded with another attack and Christiansen almost topped her fine performance with a goal on 85 minutes but her drive was deflected into the arms of the goalkeeper.
The home side finally made their pressure count with just a minute of normal time remaining. When the Blues were awarded a free-kick on the left-hand side, Christiansen floated in a dangerous cross that Brown-Finnis couldn’t hold on to. The ball dropped to the feet of the grateful Flint whose tap-in had just enough power to creep over the line.
The drama wasn't over there though. With just seconds left on the clock, Everton almost found an equaliser. With Bardsley rooted to the spot, Michelle Hinnigan struck the post in injury time and City managed to hang on for the win.
Next up for Cushing's side is a home tie against reigning FA Women's Super League champions Liverpool Ladies at the Manchester Regional Arena on 14 May. Tickets for the clash are available online or at the Etihad Stadium box office.