Posh conceded a first minute goal from a corner and fell 2-0 down after 20 minutes before Jess Driscoll pulled a goal back seven minutes before the break.
A depleted Posh side missing five regular starters fought hard in the second-half, but it was Wem who found the final goal of the game eight minutes from time to seal a deserved victory.
Four of the 13 teams in the National League are relegated at the end of the season and Posh are now fourth from bottom. They are next in action at Wem on January 9.
Wem started today’s game in blistering fashion as a superb delivery from a corner was bundled over the line from close range.
Another close-range header after impressive Posh goalkeeper Amy Butler had initially made a decent save made it 2-0 before Posh started to find their form.
Top scorer Keir Perkins volleyed over from close range before a thunderous free kick from Hannah Hipwell was tipped onto the crossbar by the visiting goalkeeper leaving Driscoll with a simple headed finish.
Driscoll was impressive throughout while Piper O’Neill played with great energy and speed down the right.
Posh created little though apart from a second decent chance for Perkins who shot over from 12 yards.
And Wem finished the stronger, striking the crossbar before sealing the points with a 12-yard shot.
Butler made two fine saves in the final stages to ensure Wem didn’t win by a bigger margin.