Goals from Lee Tomlin, Tommy Rowe and Dwight Gayle did the damage as Darren Ferguson’s side received the perfect Christmas present by lifting themselves off the foot of the Championship.
Wolves boss Stale Solbakken named Bjorn Sigurdarson on the bench following a thigh injury, but defender Georg Margreitter (hamstring) was again sidelined following another setback on the road to recovery.
And it was the hosts who showed the early intent when an outswinging corner from Jermaine Pennant after five minutes was met by Roger Johnson and his header was smartly tipped over by Posh keeper Robert Olejnik.
At the other end, Carl Ikeme in the Wolves goal had to be alert to turn away a 12-yard effort from Gayle as Ferguson’s side showed their own attacking inclinations.
It had turned into a full-blooded festive encounter with no quarter given by either side in the hunt for crucial Championship points.
And having weathered the early Wolves storm, the visitors took the lead after 17 minutes through Tomlin. Joe Newell provided the opportunity and when his cross from the left was not dealt with, in nipped Tomlin to strike home his eighth of the campaign from 12 yards.
It could have got worse for the hosts three minutes later but George Boyd cleared the bar when well placed inside the penalty box. Kevin Doyle was then ideally placed to net an equaliser but Olejnik denied the striker from only six yards.
Pennant fired over with a free-kick as Wolves looked to get back on terms before the break, but Ferguson would have been impressed with his side’s application in the opening half.
Solid in defence, Posh also looked potent on the break and seven minutes from the interval, Newell had the chance of adding a second before a well-timed block by Johnson got in the way of his 18-yard effort.
Doyle twice went close to levelling, while Stephen Ward saw his effort parried by Olejnik as the half-time whistle approached and the visitors rode their luck.
But a sucker punch at the other end of the field doubled Peterborough’s lead after 43 minutes. This time Boyd was the provider, Rowe finishing with aplomb from 20 yards.
Ward was replaced by Sigurdarson as the second half began, with Wolves well aware the next goal was crucial.
Pennant went close again for the home side, but it was Peterborough’s day and after 69 minutes Mark Little’s cross was met by Gayle to make it 3-0 and secure another valuable victory for Posh.