Ilkay Gundogan broke Everton’s stern resistance, heading home after Joao Virginia had pushed Aymeric Laporte’s effort onto the bar.
And with a minute remaining, substitute Kevin De Bruyne sealed the victory with an emphatic finish.
Everton, organised and diligent, made life difficult for City, limiting us to just a few clear openings in the first half.
In fact, Everton came the closest to scoring in the opening period when Yerry Mina’s header was cleared off the line by Oleksandr Zinchenko.
But the second-half saw City play with more fluidity. Virginia brilliantly parried Raheem Sterling’s first-time effort around the post, before Phil Foden’s left-footed strike from distance whistled inches wide.
It looked as though Everton’s diligence would take the game to extra time – but with seven minutes left on the clock, we found a breakthrough.
Laporte burst forward, played a one-two with De Bruyne, and forced a fine save from Virginia, who parried the ball onto the bar – only for Ilkay Gundogan to follow up and head home.
And a few minutes later, De Bruyne’s powerful left-footed strike confirmed our safe passage into the last four.
Everton: Virginia, Coleman, Godfrey, Holgate, Mina, Digne, Allan, Gomes, Calvert-Lewin, Sigurdsson, Richarlison
Subs: Leban, Tyrer, Broadhead, Davies, Iwobi, John, Keane, Nkounkou, Onyango
City: Steffen, Walker, Dias, Laporte, Zinchenko, Fernandinho, Gundogan (Rodrigo 89’), Bernardo (Mahrez 64’), Foden, Sterling (De Bruyne 79’), Jesus.
Subs: Ederson, Stones, Aguero, Torres, Mendy, Cancelo
New club record
17 games unbeaten away from home in all competitions. Never have City put together a run that long.
But this City squad continues to move the dial.
The previous record was set by Joe Royle’s City side between January and September of 1999 when City were playing in the third tier of English football.
That record has now been superseded by Guardiola's record-breaking side.
It’s the latest example of the mental fortitude and team ethic that runs through our squad.
City are often widely praised for the quality and brilliance of our attacking play.
We play on the front foot, dominate possession and weave some wonderful, mesmerising patterns.
But increasingly it’s our work-rate and character that is being recognised.
This was yet another example of the solidarity running through our squad. Everton were incredibly well organised, meaning this win came courtesy of our desire to win duels across the pitch and fight to recover possession when we lost the ball.
Our players desire and intensity at all times. So even when our attacking brilliance evades us, we find other ways to get results.
What it means
City progress to the FA Cup semi-final stage for the third-successive season. It’s the first time we’ve been able to say that since doing so between 1931-32 and 1933-34.
It also means we remain on course for four trophies. We are currently 14 points clear at the top of the Premier League, through to the Champions League quarter-finals and in April we will face Tottenham in the Carabao Cup final.
Having won 25 of our last 26 matches – an incredible run of form that has seen us mix artistry and industry – we have positioned ourselves superbly for a very exciting end to the campaign.
FA Cup latest
City join Southampton in the final four. Nathan Redmond inspired the Saints to a 3-0 quarter-final win away at Bournemouth earlier on Saturday.
Chelsea host Sheffield United tomorrow at 13:30, before Leicester take on Manchester United at 17:00.
Bournemouth 0-3 Southampton
Everton 0-2 Manchester City
Chelsea v Sheffield United
Leicester City v Manchester United
Top-flight domestic football will now subside for two weeks as the international game takes centre stage. As always, Guardiola will be desperate to see his players return fully fit ahead of the most important period of the season.
Our next assignment sees us travel to Leicester on Saturday 3 April in the Premier League. That game gets under way at 17:30. Leicester currently sit third in the table, 15 points adrift of City having played a game less.
Our attention then turns to the Champions League, with our quarter-final first leg against Borussia Dortmund taking place on Tuesday 6 April.
News about Everton v Man City
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Dunne: 'City are in an incredible moment'
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