Bremen came close just five minutes into the game when Santiago Garcia tested his boots from distance, but his shot flew narrowly wide.
The visitors continued to dominate as both Martin Kobylanski and Petersen came close to opening the scoring before the latter did have the ball in the net.
Clemenz Fritz found the striker in the box and he calmly finished from just six yards out.
The second half was a similar story as Hamburg's wastefulness in front of goal as well as another fine stop from Mielitz against Tomas Rincon kept the visitors ahead.
Despite both sides having chances in the second half, it was Bremen who wrapped up the points late on through Petersen.