Pope, whose disparaging Twitter post about City defender John Stones came to light after the third-round draw, nodded in a superb 35th-minute equaliser after Oleksandr Zinchenko's deflected opener.

However, Sergio Aguero ensured the hosts went in ahead at half-time before youngsters Taylor Harwood-Bellis — inadvertently scoring his first senior goal after Stones thought he had City's third — and Phil Foden sealed the Premier League champion's progress.

Nathan Smith scrambled an eighth-minute effort from Foden out of the goalmouth but fellow Vale centre-back Leon Legge was not so effective with his own last-ditch attempt, turning Zinchenko's speculative 20th-minute strike past Scott Brown.

David Silva inexplicably scuffed Ilkay Gundogan's low cross into the turf and against the crossbar with the goal at his mercy and City would rue that miss.

On a rare Vale attack, David Amoo raided down the right and Pope found space off the back of Harwood-Bellis to dispatch a fine header.

Another player who would certainly fall under Pope's self-applied label of "bagsman" is Aguero, and City's all-time record goalscorer restored his team's lead after Foden stayed just onside to steer Gundogan's chipped pass across goal.

Brown made superb early second-half saves to deny Bernardo Silva and Foden, yet City had the breathing space they desired before the hour.

Stones looked to have levelled the personal duel with Pope — in so far as there was one — but a VAR (video assistant referee) check showed his close-range shot clipped Harwood-Bellis on the line.

A wretched clearance from Stones, half-blocked by Pope, meant Vale substitute Tom Conlon almost reduced the deficit with a diving header, while David Silva's frustrating outing in front of goal continued as he dragged wide.

But Foden got the goal his efforts deserved from a drilled Angelino cross, allowing attentions to turn towards a blockbuster midweek derby.