Hammarby's best chance of extending their European adventure for the season looked to have gone, as they failed to find a way through in the goalless first leg at home a week ago.
But not only did Charleroi not make the most of having the majority of the opportunities in the first half, they allowed the visitors to break the deadlock with their only effort on goal.
With 21 minutes on the clock, a cross from the right wing was not properly cleared, and first to the loose ball was kept alive by Hampus Skoglund. He drove the byline and cut the ball back to Jusef Erabi, who applied the finish.
Hammarby held the advantage until the opening minute of the second half, when the home side got back on level terms on the night and on aggregate.
This time, it was the Hammarby defence who failed to properly clear a cross from the right side and the ball landed at the feet of Nikola Stulic at the edge of the box. His low strike evaded those in the crowded penalty area and caught out Warner Hahn in the Hammarby goal.
Though there were still almost 45 minutes to play, neither side could find a winner and extra time was needed to separate them. Paulos Abraham tested the reflexes of Martin Delavalee within minutes of the extra period beginning, before his side eventually got themselves over the line in the 119th minute.
A free-kick from wide on the right was curled into the box by Shaquille Pinas, and underneath the high, hanging ball was Victor Eriksson, who got his head to it and nodded it beyond Delavalee to send the Hammarby players and fans wild.
The 2-1 win sends the Bajen are through to the Third Qualifying Round for the first time since 2022, where they face an all-Scandinavian meeting with Rosenborg of Norway.