It was a cagey first half with few clear cut chances and both teams struggling to find space.
What opportunities that did fall came to the Brewers with Mark Duffy having a chance to test Alnwick in the Posh goal on 28 minutes and Stuart Beavon latching on to a curling cross on 30 mins but again being frustrated.
But after nabbing the two goals that put Albion in control in midweek at Blackpool, Nasser El Khayati scored another to give Albion the edge.
It was a trademark finish with the winger slotting him after jinking into the area and slotting the ball home after 36 mins.
After that Albion always looked good value for the win.
Even if Anderson had a goal disallowed in the seven mins of added time.
Albion: McLaughlin, Edwards, Cansdell-Sherrff, Mousinho, Weir, Beavon, El Khayati, McCrory, Naylor, Thiele, Duffy SUBS Matthews, Reilly, Akins, Joachim, O'Connor, Binnon-Williams, Palmer
Posh: Alnwick, Zakuani, Bostwick, Maddison, Santos, Anderson, Davey, Adebayo-Rowling, Payne, Coulibaly Subs: Curtis Henry, Brisley, Taylor, Washngton, Gormley, Angol, Sadlier