Emil Forsberg's second-half penalty sealed Sweden a 1-0 win over Slovakia in Saint Petersburg on Friday as the Scandinavians moved top of Euro 2020 Group E.
Janne Andersson's men, who played out a goalless draw with Spain in their opener, now look set to reach the knockout stage for the first time since 2004.
A point in their final game against Poland at the Krestovsky Stadium on Wednesday would be enough to be sure of a top-two finish in the group.
Slovakia could have qualified with a game to spare with a win, but still have their fate in their own hands ahead of their final match against Spain in Seville.
On Friday, Sebastian Larsson had an early effort comfortably saved by Martin Dubravka, but Slovakia otherwise started brightly, with Juraj Kucka heading wide in the fifth minute.
Both sides had spells of pressure in the first half without creating many chances, perhaps in the knowledge a point would be a reasonably good result.
Ondrej Duda made space for a shot shortly after the break, but fired over the crossbar.
Kucka drew a brilliant one-handed save from Robin Olsen, but the Slovakia midfielder was flagged offside.
It was Sweden who almost made the breakthrough twice before the hour mark, as Newcastle stopper Dubravka tipped away Ludwig Augustinsson's header and Marcus Danielson nodded over from the resulting corner.
Sweden continued to press for the winner, as Alexander Isak's header looped onto the roof of the net.
Real Sociedad striker Isak then almost scored one of the great European Championship goals, weaving past four defenders before seeing a low strike saved by Dubravka at his near post.
Sweden finally forged ahead, though, in the 77th minute, as RB Leipzig midfielder Forsberg beat Dubravka from the penalty spot after the 'keeper had brought down substitute Robin Quaison.
Slovakia laid a late siege on their opponents' goal, but saw an optimistic late penalty appeal for handball turned down as Sweden held on.