A superb volley from substitute Aidan Quinn kept up the Hatters' chances of lifting the totesport.com Combination East Division title to set up a potentially winner takes all final game against Watford on Thursday.
The Town youngster was introduced two minutes before the hour mark and lashed home 14 minutes later to extend Alan Neilson and Kevin Watson's unbeaten run in the Combination to 11 matches.
Peterborough threatened to take the lead in the first half with strike partners Edward Adjei and Appiah Kwesi forcing smart saves from Hatters goalkeeper Clarke Masters.
The Town could have gone ahead themselves before the break when trialist Gary Bowes hit the post with a shot on 23 minutes after being fed by Jack Wood.
Five minutes later, a mix-up in the Posh penalty area almost saw Taylor Nathaniel's right-wing cross elude Sam Cole in the visitors goal, but with Scott Sinclair lurking for a tap-in, the danger was cleared.
Bowes headed a decent chance over the crossbar from a Mark Farthing corner three minutes before the break as the young Hatters looked for the lead.
The second half started slowly but after Quinn and Adam Watkins' arrival from the substitutes' bench the Town gradually began to get on top.
Sinclair almost gave the Hatters the lead on the hour mark when his shot bounced inches wide of the target after he was found by Watkins.
With the score still goalless skipper Ian Roper was thrown up-front on 71 minutes and the change had the desired affect almost immediately when a minute later Quinn was on hand to smash the ball past Cole from just inside the penalty area to give the Town the lead.
The Hatters' goalscorer hobbled off injured with 14 minutes left and, as they had used all their substitutes, the hosts had to finish the game with 10 men.
As Peterborough pressed for an equaliser, Wood hacked the danger clear following Billy Crook's corner on 77 minutes and with seven minutes left Masters did well to save Danny Andrew's shot at his near post.
Despite the addition of four minutes injury time following an earlier injury to Chris Davies, the Town held on to record a vital win and ensure Thursday's game with Watford gives them a chance of lifting the title.
LutonTown: Masters, Davies, Wood, Farthing, Roper, Biggi, Nathaniel (Deeney 68), Price, Bowes (Quinn 58), Dos Santer (Watkins 58), Sinclair.
Substitutes not used: Fletcher, Barker.
Peterborough United: Cole, Watson, Bloom, Andrew, Gaughran, Piergianni, Hampson, Crook, Appiah Kwesi, Adjei, Abraham.
Substitutes: Webb, Davies, Koranteng, Austin, Dove.