There were chances aplenty in the opening minutes, with Romelu Lukaku wasting one for Domenico Tedesco’s side as he was denied by Martin Dúbravka.
Moments later, the deadlock was broken at the other end when the Falcons pounced on an error from Jérémy Doku, who passed dangerously across his own box, and although Juraj Kucka’s effort was straight at the goalkeeper, Schranz was on hand to tuck home the rebound.
Going behind did not seem to bother the Red Devils, who continued in their attempts to dictate the tempo and could have levelled when Dúbravka gifted possession to Leandro Trossard, only for the forward’s 25-yard shot to sail over the empty goal.
Amadou Onana then had a header saved and Lukaku should have equalised when stabbing wide after being sent through one-on-one, with those efforts coming either side of Lukáš Haraslín forcing a fantastic stop out of Koen Casteels at the other end with a perfectly struck volley that was palmed around the post.
The second half was all one-way traffic, but for all their dominance, Belgium – who were previously unbeaten in 14 games under Tedesco – simply found no way past Dúbravka, who made a pair of smart saves to deny Lukaku and Trossard either side of the former having a close-range effort ruled out for a narrow offside after meeting Onana’s towering knock-down.
The striker then clattered a back-post volley into the side netting before a stunning goal-line clearance from Dávid Hancko prevented Johan Bakayoko from making it 1-1.
Slovakia began to wrestle back some control in the closing exchanges, with a brilliant defensive display to thank for snuffing out a multitude of attacks.
They were given a shock when Lukaku appeared to have equalised by converting Loïs Openda’s cross, but the substitute had handled the ball in the build-up and the strike was ruled out after a VAR check.
That meant the Falcons eventually clung on to beat Belgium for the first time in their history, claiming a sixth win in their last eight outings to move into second place in Group E behind Romania, who comfortably defeated Ukraine earlier in the day.
The Red Devils, on the other hand, lose their opening group game at a European Championship for only the second time.
Flashscore Man of the Match: Dávid Hancko (Slovakia)