The three City members of the England squad all started in Gelsenkirchen as goals from Jude Bellingham and Harry Kane spared the Three Lions’ blushes.
Gareth Southgate’s side went into the contest as strong favourites but looked set for a shock exit after Ivan Schranz had given their opponents lead midway through the first half.
Slovakia were seconds from registering their first-ever knockout win at a major tournament, but a Bellingham bicycle kick in the 95th minute drew England level.
They then took the lead inside one minute of the restart when Kane headed home after a set piece situation.
It was far from plain sailing though, and England were thankful to Jordan Pickford in the opening exchanges to deny Lukas Haraslin when sent through one on one.
But the Slovakians would take a shock lead midway through the half when David Strelic threaded Schranz in behind after a ball over the England defence, confidently poking home.
It had been an out of sorts performance from the Three Lions, but they had the ball in the net soon after the restart when Foden poked home Kieran Trippier’s cutback.
But the City midfielder had made his run slightly too early, with VAR chalking off the goal for an offside.
It was unfortunate for Foden who had been one of England’s few bright points in the first 45, but Southgate’s side wouldn’t really spring to life until the final 15 minutes.
First, Foden’s sweeping corner from the left found Kane, but the captain’s header fell agonisingly wide of the post.
A few minutes later and England went even closer to that elusive equaliser, with Declan Rice crashing a long-range effort against the post before Kane’s rebound went over the bar.
It looked like the Three Lions were heading home with Foden replaced late on but, deep into stoppage time, Bellingham’s spectacular acrobatics forced a further 30 minutes.
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The looks of relief were clear on the England players’ faces, but they turned to ecstasy when Kane turned the game on its head with a close-range header from Ivan Toney’s knockdown just 50 seconds into extra time.
Kane’s substitution at the half-way point meant Walker took over captaincy responsibilities.
And the City skipper helped the Three Lions see out the win.
It means Walker, Stones, Foden and co. will face City team-mate Manuel Akanji in the quarter-finals, with England facing Switzerland on Saturday 6 July.
