Poland took an early two-goal lead in the game but were pegged back with less than 10 minutes remaining, only for Robert Lewandowski to restore their advantage with a crucial strike.
Filip Stojkovic's own goal then confirmed the result - with Poland now sure of their ticket to Russia next summer.
Fellow goalkeeper Bogdan Lobont was also unused as Romania completed their qualification campaign with a 1-1 away draw against Denmark.
Meanwhile, results elsewhere on Sunday night mean Kostas Manolas and Greece are certain of a play-off spot as long as they beat Gibraltar on Tuesday night.
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