The visitors struggled defensively and were cut open time after time by the hosts, who spurned plenty of chances before the striker - on loan from Bayern Munich - finally found his shooting boots with goals in the 85th and 88th minutes.
Neither side entered the contest in particularly good form, with Hannover's win over Wolfsburg last week halting a slide of four successive defeats while Bremen had not won in four.
It was Thomas Schaaf's side who had the first shot on goal after eight minutes, but Mehmet Ekici's deflected effort was easily gathered by goalkeeper Ron-Robert Zieler.
Moments later, the visitor's leading marksman Mame Biram Diouf had a golden chance to score in his sixth consecutive game in what was a rare attack for Hannover.
A mistake from Aaron Hunt played in the former Manchester United forward and, although he managed to beat the falling Assani Lukimya-Mulongoti, he could only shoot straight at Sebastian Mielitz.
Petersen went close as he took advantage of a dozing Johan Djourou to get on the end of a Hunt through ball, but the striker was denied by the feet of Zieler.
Bremen were in control and a minute before the break missed another chance to hit the front when Petersen volleyed over from close range after Karim Haggui mis-timed a clearance.
After their struggles to create chances in the opening period when Diouf was left isolated, Hannover almost took the lead two minutes after the restart.
Jan Schlaudraff thundered an effort towards goal with Mielitz parrying straight to Diouf, who shot straight back at the goalkeeper, who deflected the Senegalese's effort away.
Bremen wasted another chance after 55 minutes when Eljero Elia's cross was swept over the bar by Lukimya from close.
Hunt was the next Bremen player to take a shot at goal after 68 minutes but cutting in and unchallenged he shot straight at Zieler, who could easily punch to safety.
Bremen continued to press and finally beat Zieler when Papastathopoulos leapt high from a corner to outjump the stopper, but his goalbound header was cleared off the line.
It looked like Hannover would hold out but Elia progressed down the right and crossed for Petersen, who was quicker off the mark than his marker to beat Zieler at his near post.
His second was an impressive volley from inside the area thanks to neat work from Ekici as Werder picked up their seventh league win of the season, while Hannover lost their fifth straight on the road.