The Magpies goalkeeper started for his country in the Group E clash in St Petersburg, and watched on as his side went ahead through Robert Mak’s fine run and strike – though the winger wasn’t credited with the goal, as it had gone in off Wojciech Szczesny after striking the base of the post.
Dúbravka enjoyed a quiet first half against a side led by the talismanic Bayern Munich forward Robert Lewandowski, and wasn’t required to make any save of note as Slovakia held their lead until the break.
But just 30 seconds after the restart, United’s number one was beaten by Karol Linetty’s low finish after a swift attack from Poland, who posed more of a threat at the start of the second period.
Grzegorz Krychowiak picked up a second yellow card after the hour, though, giving Slovakia a chance to make the most of their numerical advantage.
And Dúbravka’s side did just that as Milan Skriniar’s well-struck effort found the bottom corner with just over 20 minutes remaining.
The Inter Milan defender’s goal gave his nation a memorable first win on their first outing at a European Championship finals, and they will now turn their attentions to their second group game against Sweden on Friday afternoon (2pm BST).
Earlier on Monday, Ryan Fraser made a substitute appearance for Scotland in their first major tournament outing since the 1998 World Cup, but couldn’t help them turn the game around as they were beaten by the Czech Republic.
The Magpies winger entered the fray midway through the second half as a replacement for Southampton’s Stuart Armstrong, with the score already 2-0 to the visitors at Hampden Park.
Patrick Schick’s fine first half header opened the scoring, and his second of the afternoon – a stunning first time strike from just inside the Scotland half – put the game beyond the hosts in Glasgow.
Fraser will now be hoping to force his way into Steve Clarke’s starting line-up for their eagerly-anticipated clash with England at Wembley on Friday night (8pm BST).
And Newcastle defender Emil Krafth was named on the bench for Sweden in their Group E opener against Spain in Seville, but came on for the final quarter of an hour.
The full back replaced Mikael Lustig after 75 minutes to help his side keep a clean sheet, with Krafth and Sweden now set for Friday's showdown with Dúbravka's Slovakia.
