The Swans welcomed back Ferrie Bodde in midfield after a five month lay-off while Shefki Kuqi continued up front after scoring the winner against Derby County last week.
With only four minutes on the clock, Kuqi turned in the area and fired low but Posh keeper Joe Lewis turned the ball round the post.
Ten minutes later Bodde tried a shot from 20 yards which whistled past the visitors upright but then an injury to Darren Pratley caused a delay as he received treatment.
While he was off the field, Cotterill raced through the middle in the 18th minute surrounded by four Posh defenders and, when he fell to the ground, referee Gavin Ward signalled a penalty. Cotterill slammed the spot-kick into the corner to give the Swans an early lead.
Pratley never returned and was replaced by Mark Gower and he was quickly followed on to the field by Lee Trundle who went on for the unfortunate Bodde who limped off on the half-hour with knee damage.
With the first half drawing to a close, Exodus Geohaghon gifted the ball to Kuqi whose shot was blocked. The loose ball ran out to Nathan Dyer but his goalbound strike was cleared off the line by the relieved Geohaghon.
Seven minutes after the break Dyer raced down the right before crossing to Kuqi but his first-time shot went high over the bar when well placed.
Posh were pinned back in defence for long periods but the Swans were unable to make their superiority count and both Trundle and Kuqi wasted opportunities to put the game beyond their visitors.
Trundle did bring a superb stop from Lewis in the 70th minute and then Kuqi bustled his way through but a lack of control saw the chance go begging.
Lewis came to his side's rescue in the 79th minute when he leapt to his right to turn away a goalbound drive from Trundle.
It was another three points as the Swans maintained their push for promotion but they may still rue their lack of goals which kept the division's bottom club in the game until the death.