Vladimir Darida stepped up from 12 yards to take advantage of the mistake with an emphatic finish.
Bremen responded well to the early setback, and managed to draw level just after the half hour mark when Franco Di Santo slotted home his fourth of the season from Zlatko Junuzovic's defence-splitting pass.
The Argentine should have put his side ahead before the break with a second goal, but he could only slice wide of the target from just inside the box.
Freiburg copied their start to the match with an extended spell of pressure in the second half kicked off by Jonathan Schmid's powerful strike against the post.
However, Bremen came back strongly once again, and Roman Burki was forced into action to keep out Di Santo's low effort from close range.
It was the home side who piled the pressure on in the closing stages as they searched for the winning goal, but time would run out for Robin Dutt's side, meaning both teams are still waiting for their first victory of the season.