Posh triumphed thanks to midfielder Joe Newell’s calm left-footed finish and youngster Jonathan Edwards 18-yard strike.
An even first half saw Edwards’ shot saved, while Jack Friend’s deflected effort was also some concern for Luton’s back-line.
Posh played at a far greater tempo in the second half and created a number of opportunities with Edwards, Friend and Newell all going close before the latter produced a fine finish following a good pass from Craig Alcock.
Peterborough keeper Joe Day produced a couple of fine saves to keep the London Road outfit ahead before Edwards wrapped up the win.
Posh: Day, Santos, Alcock, Grant, Ntlhe, Payne, Newell (Conlon), Anderson, Trialist, Friend (Coulson), Edwards.