The hosts could have made it 2-0 just before the 10-minute mark but Leon Balogun's header from an Axel Bellinghausen free kick went well over the bar.
However, just after 15 minutes Bremen were level as Zlatko Junuzovic finished off a quick counter-attack by sweeping the ball into the top corner.
After the equaliser, chances died down a little until right at the end of the half when a Johannes van den Bergh shot went just over the bar.
Just after the restart the hosts went hack in front when Andreas Lambertz found Reisinger in the box and he made no mistake with his finish.
They were unable to hold on to the lead for the second time, however, as this time centre-back Martin Latka diverted the ball past his own goalkeeper.