The away side have only lost one game all season - and are guaranteed promotion with three games to spare, but they were pushed all the way by their hosts.
Luton’s defensive flaws meant Peterborough opened the scoring within the first eight minutes but Jamie Hyde’s try meant that the home side were immediately back in the match.
As is the way with Luton at times, it was a case of one step forward two steps back when good play would quickly unravel and the league champions racked up the points.
Peterborough’s clinical play meant that the home side were punished hard for their mistakes, trailing 24-5 at the interval.
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Luton’s coaching staff must have given a great half time talk as a different team came out for the second period.
The defeated attitude from matches before was replaced with determination and belief that the hosts could turn the game around, as they almost did.
Winger Aiden Kenny was explosive with his pace and left the champion’s defence with little answer, as he grabbed five points with David Hamm slotting the conversion.
Peterborough tried to extend their slim advantage but Luton’s grit came through as scrum-half Johnny Wright scored the first of his two tries.
However, a brilliant run by Martin O’Grady was cut short and he was carried off with what looked like a leg injury.
Hamm scored the subsequent penalty to ensure only four points separated the teams with 17 minutes to go.
The visitors then displayed their champion’s credentials and scored a converted try, as although Joe Murphy brilliantly went over in the dying moments, it wasn’t quite enough.
Afterwards, coach Nick Rhodes said: “We could have won the game.
“The team played very well, they played for each other and the guys seem like they are enjoying it.”
Luton travel to rock bottom Rushden and Higham on Saturday.