After three insipid group-stage performances, Southgate’s side were searching for a display which would reignite hopes of winning a first major trophy in 58 years.
However, the start here did nothing to inspire that confidence, with England looking defensively vulnerable as Dávid Hancko and Lukáš Haraslín threatened to open the scoring for Slovakia, with the latter denied by a last-ditch challenge from Marc Guéhi.
England rallied with chances for Harry Kane and Kobbie Mainoo, but Southgate’s growing number of critics sharpened their knives when Francesco Calzona’s side took a well-deserved lead.
David Strelec threaded an intricate through ball into the path of Ivan Schranz to apply a clinical finish with the outside of his right foot, taking his personal goal tally for the tournament to three.
Despite failing to register a shot on target in the first half of a knockout game for the first time since 1986, there were no England changes at the break.
Phil Foden saw a strike ruled out for offside within minutes of the restart, but Slovakia were undeterred, threatening a second in audacious circumstances. Strelec intercepted an unforgivably sloppy short free-kick from Kyle Walker towards John Stones and let fly from the halfway line, but his strike drifted wide of Jordan Pickford’s goal.
Cole Palmer was introduced for Trippier in a bid to add some much-needed fresh impetus, yet Slovakia goalkeeper Martin Dúbravka remained completely untroubled.
He should have been called into action when Kane met Foden’s perfectly-weighted free-kick, but the England captain inexplicably headed wide. Declan Rice then rifled a long-range strike onto the post to spark some late hope of salvation, but England had still failed to register a shot on target heading into the final 10 minutes.
However, just when the Three Lions looked to be heading out of the tournament with a whimper, Jude Bellingham - as he has done so often for Real Madrid all season - netted in stoppage time, levelling the scoreline with an outstanding acrobatic finish after Guéhi flicked on Walker’s long throw into the box.
It was England’s first shot on target of the match, and it arrived in some style to take this contest into extra-time.
Suddenly, this game had taken a dramatic twist, as just 52 seconds into extra-time, Kane headed home from inside the six-yard box after subsitute Ivan Toney flicked to fellow late arrival Eberechi Eze whose miss-hit shot fell into the skipper’s path.
It completed the most remarkable of turnarounds, denying Slovakia what would have been their first appearance in the quarter-finals of a major tournament as an independent nation, while Southgate’s charges will head into the last-eight to face Switzerland in Düsseldorf on Saturday with their morale lifted.
Flashscore Man of the Match: Jude Bellingham (England)