David Martin smashed home a first-half penalty at the third time of asking after Gary Alexander had been unlawfully denied twice by Posh keeper Joe Lewis who crept off his goal-line.
Winger Martin then turned provider to tee up on-loan striker - and star of the show - Jason Price to tap home a second as the Lions continued to keep the door closed on Darren Ferguson's side.
Ferguson was quite rightly furious with referee Keith Woolmer and his assistant Mr Creighton for handing the Lions three attempts from the spot after Lewis was adjudged to have crept too far off his line both times to keep out Alexander.
The controversial penalty was correctly awarded on 25 minutes when Martin was tripped in the box by Dean Keates as the winger was set to fire home Price's excellent cut-back. Up stepped Alexander to hammer not once, but twice straight at Lewis as he drifted off his line.
The third, this time from Martin, was simply unstoppable as he placed his left-foot effort into the top corner to send the home fans delirious.
The strike partnership of Aaron McLean and Craig Mackail-Smith had failed to trouble the resilient backline all evening with only the odd pot-shot from distance registering on David Forde's goal.
Ten minutes after the opener, Keates almost made amends for his mistake for the Lions penalty. His left-footed free-kick from the edge of the box whistled just over the crossbar with Forde well beaten after Tony Craig's foul on Mackail-Smith.
The Lions headed into the break with the wind in their sails and their determination and harassing of the Posh backline made it very uncomfortable for the visitors.
The Lions should have been awarded a second penalty five minutes after the break when sub Chris Westwood appeared to handle a volley in the Peterborough box.
But the breathing space for the Lions came with the second goal just before the hour mark as Price tapped home his third in five appearances since joining from Doncaster.
Dave Martin had left his namesake Russell for dead down the Lions left after some good pressure by Alexander. Young Martin then got to the byline before picking out a delicate chipped cross to the far post for the Welshman to gratefully tuck home and seal the points.
From then on in it was plain-sailing for the hosts with their 10,000-strong crowd behind them to the final whistle.
McLean had time for just one chance for a consolation goal. He latched on to Keates' defence-splitting pass with ten minutes to go but fired straight at Forde with the whole goal to aim at.
But the result was in the bag to leave south London vibrant as the final weeks of the season still have plenty in store for both sides.