Slovakia started much sharper than England, giving their opponents several warnings before Ivan Schranz placed a deft finish past Jordan Pickford in the 25th minute.
The last three Euro games in which England conceded first, including the last edition’s semi-final, were won by England. After the break, they thought they were level, but Phil Foden’s mistake was obvious, as he tapped home.
Harry Kane headed a Foden free kick wide, and Declan Rice hit the post as Slovakia were pinned deep in their own half late on. England seemed to lack belief as their fans grew ever more frustrated.
However, Bellingham, a day after his 21st birthday, equalised with a bicycle kick at the death, taking the game to extra time with England’s first shot on target.
It took England less than a minute to take the lead when Kane smashed past Martin Dubravka from close range, completing a remarkable turnaround.
As the game progressed, Slovakia began to falter and came closest to a comeback when Peter Pekarik slid a dangerous cross over the bar just before halftime in extra time.
England repelled a late wave of balls into the box to secure a lucky victory and set up a quarter-final clash with Switzerland in Duesseldorf on Saturday.
They will need to perform much better against the Swiss, who outplayed Italy in the last-16 and conceded a late equaliser against Germany in the group stage.
After their last-16 match was delayed by a thunderstorm, Kai Havertz and Jamal Musiala scored in the second half to send Germany into the quarter-finals with a 2-0 win over Denmark.
The game was halted for 20 minutes in the first half due to the weather, and Danish defender Joachim Andersen went from hero to zero shortly after the break when his close-range finish was disallowed for offside, and he conceded a penalty that was converted by Havertz in the 53rd minute.
Germany established an unassailable lead in the 68th minute when Musiala ran onto a ball over the top and curled home his third goal of the tournament.
Denmark chased the equaliser and were often exposed to counter-attacks after Havertz scored with a tidy finish. Musiala did not waste his opportunity, as Havertz and Leroy Sane missed close-range chances, but Musiala did not waste his opportunity. Germany’s spot in the quarter-finals was secured by him bursting onto a long pass and finishing calmly past Kasper Schmeichel.