After a scrappy opening few minutes at London Road, Peterborough's Paul Taylor had the first meaningful effort on goal. The winger picked up possession just inside Posh's half before beating two players and sending his effort just wide of Simon Mignolet's goal.
Having scored his first goal for Sunderland against Wigan Athletic last week, James McClean went close to adding his second when he rattled the crossbar from the edge of the area with half-time fast approaching.
Sunderland's victory was confirmed in the space of ten second-half minutes, with Swede Larsson heavily involved in both.
Firstly his free-kick from the left touchline evaded everyone, including Peterborough goalkeeper Joe Lewis, as the ball nestled in the bottom corner with 47 minutes played.
Then it was his corner that was met by McClean, who headed the ball into the roof of the net from close range.
The home side offered little threat as the match drew to a close and it was Sunderland that looked the more likely to find the net.