The 1-0 goal came after 55 minutes.
Just seven minutes later, the Dane Jeppe Andersen received his second yellow card.
With ten players, the uphill became too steep for Hammarby and they were never close to an equalizer.
Instead, Jakub Kaminski extended it to 2-0 with a resolute shot in the 89th minute.
He extended it to 3-0 with a rock hard shot in overtime.
Good Start
Hammarby otherwise started well and grabbed the match.
The first half was even in terms of play but it was Hammarby who had the hot chances.
Aron Johannsson came close to extending the visitors' lead when he found himself completely unmarked in front of the goal after a pass through the middle, but he lifted the ball over Johann Ludwigson and it was a little too high and hit the bar.
The text is updated.
KLIPP: Hammarby won comfortably against Puskas Akademia
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Hammarby won in the Europa League qualifier before the eyes of Zlatan Ibrahimovic.
Photo: Bildbyrån