The United States star struck seven minutes into the second half to open her account and level the score, before Chloe Kelly continued her superb scoring streak to turn the tie against her former Club and youngster Jess Park sealed the victory with a thumping finish.
Danielle Turner had broken the deadlock on 20 minutes but the home side produced a spirited display to turn the game on its head and kick off our Group C campaign on a positive note.
The triumph marked further good news for City, as Karen Bardsley made her first competitive appearance since the 2019 World Cup.
Much of the pre-match talk had deemed this clash as a ‘warm-up’ for the 2019/20 FA Cup Final at the start of November.
Both sides headed into the encounter in excellent form with Everton boasting a 100% record and City triumphant in four of our five games.
With both sides on a roll and full of confidence, the game exploded into an all-action, fast-paced start.
Inside the opening six minutes, Kelly had forced Tinja-Riikka Korpela into two fine stops at her near post, before Lavelle headed off-target.
Everton’s best chance of the opening exchanges had been a speculative long-range looping effort but the visitors took the lead against the run of play on the 20-minute mark, as an unmarked Turner stole in at the backpost.
The strike stunned the hosts, who had dominated, and City struggled to muster any clear-cut chances for a first-half leveller, and headed into the break trailing.
As was the case against Tottenham Hotspur on Sunday, the home side came flying out of the blocks in the second half.
Kelly cut inside – only to be denied once again by Korpela – while Alex Greenwood was inches away from her first City goal, curling a free-kick just over the bar.
The hosts would find the net courtesy of a set-piece, as Lavelle flicked Greenwood’s corner past Korpela at the near post.
Lively youngster Park then saw a deflected effort well-saved, while at the other end, Bardsley had to be alert to thwart Nicoline Sorensen and Valerie Gauvin.
Just when the clash looked to be heading for a draw and a penalty shoot-out, Georgia Stanway drove at the Everton defence before coolly slotting into the path of Kelly to convert from close range.
Park then capped a superb individual display to weave her way into the box and smash beyond Korpela to clinch all three points.
What it means
City go level on points with Liverpool in Group C, after the Reds also defeated Manchester United 3-1 earlier in the day.
How we lined up
In the midst of a crunch period of fixtures, Taylor opted to make six changes to the side which defeated Spurs 4-1 on Sunday.
Kelly faced her former club on the left flank, with Park on the right, while Stanway led the line upfront.
Player of the Match
Showcasing blistering pace, trickery and a fearless composure beyond her years, 18-year-old Jess Park produced a very impressive display, chasing down every ball and looking to mount an attack at every opportunity.
She scored the goal her performance deserved in injury time with excellent footwork and a thundering finish.
Chloe Kelly's strike marked City's 100th goal in the competition.
The win also continues our exceptional record against the Toffees with 13 victories from 13, since we joined the FA Women's Super League in 2014.
Of those 13 encounters, we've netted 34 goals, conceding just seven.
City face our toughest test of the season so far, travelling to WSL title challengers Chelsea on Sunday 11 October.
It’s a 2:30pm UK time kick-off at Kingsmeadow and the game will be shown live via BT Sport.