Gareth Southgate's men flattered to deceive for the fourth game running in Germany and appeared to be heading for a deserved exit when Ivan Schranz slotted in his third goal of the competition.
However, a last-gasp Jude Bellingham bicycle kick forced an additional 30, the first minute of which saw Harry Kane come up with a critical captain's contribution, heading in the goal that sealed England's spot in the last eight.
The Three Lions have now progressed to the quarter-finals of all four major tournaments with Southgate at the helm, and here, Sports Mole analyses England's nail-biting success at the Veltins-Arena.
HIGHLIGHTS
5th min: Lukas Haraslin and David Hancko link up well down the left as the latter fizzes a crisp ball across the six-yard box, but there are no takers.
9th min: Jude Bellingham plays a stunning cross-field pass to Kieran Trippier, who is in acres of space and goes for the first-time strike but balloons his effort into orbit.
12th min: Slovakia break down the left again through Haraslin, who speeds away from Walker and finds himself one-on-one with Jordan Pickford, but Marc Guehi comes charging in to take the sting out of the shot and Trippier can hack clear.
23rd min: Trippier's inswinging cross reaches Harry Kane at the back post, but Hancko manages to get his shoulder in the way to deflect the ball behind for a corner.
24th min: Kobbie Mainoo tries the spectacular on the half-volley and his effort is not a million miles away, but still too high to trouble Martin Dubravka.
GOAL: ENGLAND 0-1 SLOVAKIA (SCHRANZ)
25th min: A third goal of the Championships for Slovakia winger Ivan Schranz! David Strelec holds the ball up well in front of John Stones and waits for the run of Schranz, who is ahead of the booked Guehi and Trippier and pokes the ball into the bottom corner. 0-1.
45 +3 min: Mainoo works some space with a fine solo run from the left channel and lets fly, but his shot takes a nick on its way behind.
HALF TIME: ENGLAND 0-1 SLOVAKIA
50th min: England finally penetrate the Slovakia backline to devastating effect, as Kane sprays a delightful ball out to Trippier, who squares for Phil Foden to tap home, but the Manchester City man was ahead of the last defender and the goal is chalked off for offside.
52nd min: Kane's low strike takes a wicked deflection off of Denis Vavro and drops just wide of Dubravka's far post. England much better at the start of the second period.
55th min: Nearly a calamity for England as Stones fails to spot a short Bellingham free kick roll in front of him, and Strelec's audacious effort from the halfway line bounces just wide.
59th min: Controversy as a yellow-carded Juraj Kucka scythes down the bright Mainoo on the edge of the box, but the referee decides against sending off the Slovakia midfielder.
78th min: A golden chance for Harry Kane goes begging as the Bayern Munich man somehow heads wide of the post from a brilliant free-kick delivery from Foden.
81st min: A 20-yard drive from Declan Rice smacks the post before Kane's acrobatic rebound bounces once and flies over the top.
87th min: Stanislav Lobotka goes for a drive from range which is straight down Pickford's throat.
GOAL: ENGLAND 1-1 SLOVAKIA (BELLINGHAM)
90 +5 min: Bellingham saves England right at the death with one of the goals of the tournament! A Walker long throw is nodded onto the Real Madrid man by Guehi, and he leaves Dubravka flat-footed with a magnificent bicycle kick into the bottom corner!
FULL TIME: ENGLAND 1-1 SLOVAKIA
GOAL: ENGLAND 2-1 SLOVAKIA (KANE)
91st min: Two shots on target, two goals for a revived England! Slovakia can only partially clear their lines after a set-piece, and Eberechi Eze's volley into the ground is nodded on by Ivan Toney, whose header finds captain Kane to guide home!
105th min: Slovakia right-back Peter Pekarik is in a fantastic position to score at the back stick as a ball is fizzed into him, but under pressure from Eberechi Eze, he deflects Laszlo Benes's cross over the top.
111th min: Lubomir Tupta goes for goal from a 25-yard free kick, but it is too central and too high to cause Pickford any problems.
FULL TIME IN EXTRA TIME: ENGLAND 2-1 SLOVAKIA
MAN OF THE MATCH - DECLAN RICE
Of course, a mention for Kobbie Mainoo, England's two goalscorers and Slovakia's entire backline, but the Three Lions would not have progressed had it not been for the flawless efforts of Declan Rice in the middle.
The Arsenal man did not misplace a single long pass (7/7) or lose a single ground duel (6/6) in a tough-tackling display, although his fracas with Calzona at the end was an unnecessary blot on the notebook.
STANDOUT MOMENT
Having looked leggy, unproductive and in desperate need of a rest during England's draws with Denmark and Slovenia, some even suggested that Jude Bellingham ought to have been dropped for the last 16, pleas that of course fell on deaf ears.
After nearly allowing Strelec to score from the halfway line with a careless free kick, the 21-year-old spared England's blushes with a perfectly-executed bicycle kick, in what will no doubt be remembered as one of the goals of the tournament.
BEST STATS
MATCH STATS
Possession: England 63%-36% Slovakia
Shots: England 16-13 Slovakia
Shots on target: England 2-3 Slovakia
Corners: England 9-1 Slovakia
Fouls: England 12-19 Slovakia
LINEUPS
ENGLAND (4-2-3-1): Pickford; Walker, Stones, Guehi, Trippier (Palmer 66'); Mainoo (Eze 84'), Rice; Saka, Bellingham (Konsa 106'), Foden (Toney 90 +4'); Kane (Gallagher 106')
SLOVAKIA (4-3-3): Dubravka; Pekarik (Tupta 109'), Vavro, Skriniar, Hancko; Kucka (Bero 82'), Lobotka, Duda (Benes 82'); Schranz (Gyomber 90 +3'), Strelec (Bozenik 61'), Haraslin (Suslov 61')