Darren Ferguson piled praise on his “relentless” Peterborough players after they followed up EFL Trophy success by boosting their automatic promotion bid.
Posh jumped to within six points of second-placed Derby – and also boast two games in hand – by brushing aside struggling Vale.
Joel Randall broke the deadlock in the final seconds of the first half with a blast that took a double deflection on its way past Connor Ripley after Harrison Burrows’ short corner.
EFL Trophy final hero Burrows doubled the advantage from the penalty spot 11 minutes into the second half and the Posh captain was again the architect when his 86th-minute cross was headed into his own net by Alex Iacovitti to compound Vale’s misery as they dropped back into the bottom four on goal difference.
Delighted Posh boss Ferguson said: “That is as well as we have played at home for a long time.
“It was a really good performance from my team… mature, confident, some great football and a clean sheet.
“We didn’t panic when the first goal took a while to come and then we had complete control in the second half.
“I was really pleased with the result but the manner of the performance at this stage of the season is what delighted me the most.
“People might have wondered what we would look like after Sunday but we were so fresh physically and running all over them.
“These lads are relentless. I have to give them and the staff a lot of credit.
“We know Derby drew and dropped points but we just keep looking at the next game. I’ve already watched Oxford today and we’ll look no further ahead than that on Saturday.”
Vale boss Darren Moore admitted: “It was a difficult night for us.
“If we could have got to the break with the scores level, it might have created a bit of anxiety around the place.
“But the first goal on the stroke of half time really changed my team-talk and gave us a mountain to climb in the second half.
“Peterborough are an excellent and free-scoring team with a lot of attacking options and move the ball really well. Up to a point, the boys stuck to the gameplan to nullify and contain them well.
“It’s just disappointing to concede the first and second goals in the manner we did from corners as we’d worked on that.
“The first goal took two deflections and the second one is a switch-off at the far post which leads to a penalty.
“The third one is then an own goal but I’ve got no complaints in terms of the commitment and energy the boys showed.”