The defeat left the Poles stuck at the bottom of their four-team qualifying group with one point.
Sweden scored early in both halves before a brilliant strike by Robert Lewandowski, which made amends for an earlier miss, brought Poland back into the match.
Lewandowski twisted to score again in the 84th minute, setting up a grand-stand finish as the Poles pushed to find the goal that would take them into the second round.
But the Swedes held on, and scored their third in the 94th minute to send the Poles packing.
The first round elimination is a disappointing result for the Polish national team, which started the tournament in a confident frame of mind. Only a battling draw with Spain provided some consolation. (PAP)