The hosts took the lead as early as the eighth minute through Edu.
Sebastian Prodl thought that he had equalised just two minutes later with a header, but he was adjudged to have committed a foul in the build-up to his goal.
However, Grun failed to keep out Petersen a minute before the half-time interval when the German striker headed home Arnautovic's cross from just five yards out.
Five minutes into the restart Petersen could have scored his second goal of the afternoon, but he could not keep his shot on target.
The 23-year-old was denied by Grun again in the 59th minute, before Thomas Kleine headed wide for Furth on 68 minutes.