Despite starting brightly, the hosts found themselves increasingly on the back foot as Strasbourg started to grow into the game, and Rafael Luis fired off an early warning with a curling effort from distance.
The opener came shortly afterwards, with Martial Godo the creator on the left flank. It initially looked like he might be crowded out as the home side were back in numbers and well-positioned, but a pinpoint cross picked out Julio Enciso, and the Paraguayan expertly guided the ball into the corner of the net midway through the half.
Hacken tried to find a leveller before HT, but the French side looked comfortable in possession and safely carried the lead into the break.
Though his side held the lead, Liam Rosenior made three changes at the break, but it didn’t halt their momentum as Strasbourg doubled the lead just before the hour mark.
Initially, it looked like Godo had passed up the opportunity when he took a wild swipe and missed the ball in the six-yard box, but it broke kindly for him to tap home at the second attempt.
Just when it looked like the game could be over, the Swedish side responded immediately. Mike Penders failed to make a decisive decision when faced with a long hopeful ball, allowing John Paul Dembe to nip in and prod past the keeper into the empty net.
The game began to stretch in the final 10 minutes, with Hacken looking for a leveller and the visitors seeking a third to seal the win.
Mikkel Rygaard went close as his left-footed shot curled just over the bar, but that was the closest they came to completing the comeback.
The result leaves Hacken searching for their first win in this year’s league phase after drawing their opening two games. On the other hand, Strasbourg look well-placed to make it through to the knockout phase, sitting inside the top eight with seven points from three games.