The home side were dominant in the first half and they could have taken an early lead when Assani Lukimya-Mulongoti's header came back off the crossbar.
Zlatko Junuzovic and Petersen both missed decent opportunities for Bremen as they lacked a clinical touch in front of goal.
An evenly-matched second half saw Lukimya-Mulongoti's effort loop narrowly over the bar before Sokratis Papastathopoulos had his header cleared off the line.
With the game looking like it would end all square, Petersen smashed in Eljero Elia's cross in the 86th minute to put Bremen ahead.
The striker then added a second minutes later with a volley to wrap up the win for his side.