Hungary moved to the top of Group A3 with a victory over Germany.
Adam Szalai scored the winning goal as he met a corner with a backheeled flick.
The 34-year-old is set to retire after Monday's final group game saying he had been "looking for the right time" in his pre-match news conference.
Hungary will play Italy in their final group game knowing a draw will see them through.
Italy's win over England in Milan means qualification will be decided between the two teams on Monday.
Hungary has a great record in the Nations League. Back-to-back promotions have seen them rise to League A and they are poised to qualify for the finals for the first time.
Hungary took the lead through Szalai's 26th international goal, but Willi Orban's effort was well smothered by ter Stegen in the first half.
It took Germany until the 39th minute to register a shot on target, as Thomas Muller's back-post headed was easily saved by Peter Gulacsi.
The hosts had 80% possession in the first 15 minutes of the second period after Hansi Flick made a tactical change at the half-time break.
Sane's effort was saved at the near post before Muller's 20-yard volley was ruled out for being inaudible.
Hungary came closest to extending their lead with Martin Adam and Laszlo Kleinheisler having their goals saved.
Germany will remain in League A despite being unable to qualify for the finals due to the defeat.
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