After a quiet start to the game, Sammie Szmodics took charge to play a key part, opening the scoring in the 25th minute with a cool finish from a Siriki Dembele assist. He was also heavily involved in the second goal, just over five minutes later, steering the ball across the face of goal for Jonson Clarke-Harris to tap in.
Crewe boss David Artell made a triple substitution just before the hour as his side searched for a reply - and it almost had an immediate pay-off when the newly-introduced Stephen Walker delivered a cross that Owen Dale headed over from close range.
The visitors never came closer than that, though, and Posh missed further chances from to extend the lead in the second half.
After the game, Artell expressed his outrage at what he described as a 'broken leg tackle'. He said: "Goals change games and we’ve conceded in almost identical fashion twice. For that to happen once is bad, but for it to then happen again a few minutes later is criminal.
"We have to make sure we understand why the game went away from us and didn’t get back into it. We didn’t use our brains enough and we’ve got to be better – it’s as simple as that.
"But the game should have changed on 47 minutes when their lad made a broken leg tackle and yet the referee gave a yellow card. We had a lad with a broken leg in midweek and we’ve just seen another broken leg tackle this afternoon and yet the referee gives a yellow card.
"If he doesn’t think that’s reckless and endangering an opponent... it’s only because an experienced midfielder gets out of the way of it. It’s an horrific challenge."
Peterborough boss Darren Ferguson was understandably pleased in his post-match comments. He said: "I am very pleased with the victory and another clean sheet.
"We scored two good goals and could have scored more to perhaps kill the game off in the second half. It was a little frustrating we didn’t do that, but I am delighted with the players overall as they put a real shift in.
"The front three combined really well and I thought Sammie in particular was brilliant. He scored one, created the other and his energy was superb. He got into some great positions and linked the play really well.
On the difficult state of the Posh pitch, which has been hit with drainage issues since before Christmas, Ferguson stated: "Everyone knows it is a heavy pitch, but that is not causing us any problems at the minute in terms of the performances. We are creating chances, scoring goals and keeping clean sheets on it, but we know we are going to need everyone to play their part."
After successive defeats to Shrewsbury and Tranmere a win was desperately needed for Peterborough, who move up into fourth place in the league after Portsmouth faltered to Plymouth. Lincoln City remain top with 51 points to Peterborough United's 46.