Aidy Boothroyd’s men struggled to a goalless draw against Sweden in the tournament opener on Friday night and looked on the brink of an early flight home when Martin Chrien netted for the Slovaks.
But Alfie Mawson’s tap in and Nathan Redmond’s wonderful finish make sure they have a top chance of qualifying for the semi-finals when they face Poland on Thursday.
Martin Chrien had given Slovakia a deserved first half lead when he expertly flicked a corner past Everton’s £30m new boy Jordan Pickford.
The Viktoria Plzen midfielder charging in at the near post to loop the set-piece into the goal as the Young Lions disappointed in the first half.
But they improved after the interval as Swansea defender Mawson reacted quickest after the Slovakian keeper parried Jacob Murphy’s stunning in-swinging cross in the 50th minute.
Eleven minutes later captain James Ward-Prowse produced a raking cross field ball to find Southampton teammate Redmond.
The winger cut back onto this right foot to beat a defender before smashing into the top corner to hand England the three points.
There was a nervy moment late on then Murphy appeared to handle in the box – but the ref didn’t spot the incident.