Dave Robertson's men slipped to only their second defeat in seven games as Coventry City claimed a 1-0 success at the ABAX Stadium in a fixture that lacked any real quality.
It was Dominic Samuel who had the first effort of the game, but his 20-yard shot went wide of the post after some hesitant Posh defending.
Both sides were struggling to come to terms with the weather conditions and the bobbly surface and as a result for 15 minutes, it became very scrappy with very few passages of pleasing football.
A good piece of individual play by Michael Bostwick created a crossing opportunity for Smith down the right, but despite five Posh players to pick out in the box, it was goalkeeper Burge who came to collect.
Jack Payne saw a 20-yard shot deflected behind for a corner kick on 37 minutes. The visitors were forced into a substitution on 41 minutes as Tudgay was forced off with an injury, Odelusi the man to replace him.
Samuel scooped over the bar from the edge of the box on the stroke of half-time as referee Mr Williamson brought an end to a first half lacking in any real quality.
Posh made a change at the break with Luke Williams replacing Washington in attack. Williams fired wide from 35-yards on 50 minutes after collecting a pass from Ntlhe in a central area.
Jack Payne found the side-netting with a shot from distance as Posh looked livelier in their attacking play, backed by a noisy home support.
Alnwick made a routine stop at the other end to keep out a low shot from Fleck who had ghosted into a decent shooting space.
The lively Williams saw a fierce drive beaten away by Burge on 63 minutes after a sharp turn on the edge of the box. Marcus Maddison replaced Newell on 67 minutes.
On 70 minutes, the visitors found a breakthrough as a shot from Odelusi was deflected and spun kindly into the path of fellow substitute TURGOTT who guided the ball past Alnwick.
Payne was denied an equaliser by a sprawling save from Burge on 73 minutes after letting fly with a dipping volley from distance.
A clever pass from Williams picked out James moments later, but from a tight angle his shot was parried by goalkeeper Burge.
Burgess saw a shot on the turn blocked as Posh tried to push men forward. Harry Anderson replaced Brisley in the final attacking change, but Posh were struggling to get ahead of steam.
Samuel found the side-netting at the other end following a deep cross to the back post.
Full-time: Peterborough United 0-1 Coventry City
Posh: Alnwick, Smith, Ntlhe, Brisley (sub Anderson 86min), Bostwick, Taylor, Payne, James, Washington (sub Williams 46min), Newell (sub Maddison 67min), Burgess. Unused subs: Henry, Sheehan, Pearson, Beautyman.
Coventry: Burge, Willis, Fleck, Ward, O'Brien (sub Webster 90min), Samuel, Nouble (sub Turgott 60min), Tudgay (sub Odelusi 41min), Martin, Pennington, Stokes. Unused subs: Charles-Cook, Thomas, Barton, Phillips.
Attendance: 7,325 (836 Coventry fans).