Victory for England over tournament hosts Poland denied Slovakia the chance of automatically making it through, but they did what was required to remain alive in the Under-21 European Championships.
Slovakia, whose crushing victory brings an end to defending champions Sweden's campaign, are now left relying on other results in the hope of going through as the best-placed runners-up.
The 2000 semi-finalists dominated the first half, taking just five minutes to open the scoring through a Martin Chrien header at the back post following some slack defending.
The corner was worked short and the ball made its way to the Viktoria Plzen midfielder, who was left with the simple task of stooping in to bag his second goal of the competition.
Sweden were barely able to make it out of their own half of the field, being given an even bigger mountain to climb 22 minutes in after Jaroslav Mihalik blasted past Anton Cajtoft at the end of a swift counter to double his side's advantage.
Mihalik in particular was having plenty of joy down the left-hand flank, sending in a teasing cross 40 minutes in for Matus Bero to guide narrowly wide of the far post with his head.
Bero came even closer from the final act of the one-sided first half by testing Cajtoft with a punt right down the middle, and the same player was involved soon after the restart to divert Chrien's cross wide.
Slovakia's dominance deserved a third goal, but they were unable to create too many clear-cut chances and allowed their opponents to grow into things a little more as the hour mark approached.
Sweden, who finished above Spain en route to qualifying for the tournament, were showing few signs of quality in attack and saw their slender hopes of progression come to an end 17 minutes from time.
Former Newcastle United man Lubomir Satka rifled the ball into the bottom corner from the edge of the box to give Pavel Hapal's men a third goal, leaving them in a strong position to go through in second place.
Chovan was later required twice in quick succession to thwart substitute Joel Asoro and Carlos Strandberg, the latter of whom was essentially clean through on goal when seeing his shot kept out down low.
That proved to be it in terms of the chances, leaving Slovakia relying on other results to take them through to the last four.