Darlington were unstoppable after grabbing the lead inside the second minute. Gaetano Giallanza's pace was too much for Chris Plummer and after the Swiss striker was upended, Barry Conlon fired his fifth goal of campaign into the roof of the net from the penalty spot.
It needed a smart save from goalkeeper Mark Tyler to deny Conlon a second after Joachim beat the home offside trap. But the best was still to come from the one-time £1.5million man when he was signed by Leicester City.
Joachim picked up the ball close to the centre circle on 21 minutes and carved his way through the Posh defence, ghosting past Mark Arber on a 40-yard run before netting Darlo's second with a delightfully struck shot with the outside of his right boot.
A poor clearance from Guy Branston let in Darlington for a third goal just three minutes later. Joachim intercepted just inside the penalty area and after exchanging passes with Giallanza was almost able to walk the ball into the net.
Despite their problems at the back Posh did create chances with Justin Richards and Lloyd Opara denied by Sam Russell in the Darlington goal, with Danny Crow sending a fierce drive just over.
Posh posed more of a threat after the break and Darlington were glad of smart saves from Russell to deny Trevor Benjamin and Opara who also hit the woodwork.
But three minutes after Giallanza was shown a 77th minute straight red for retaliation on Adam Newton who was cautioned, Crow managed to pull one back, firing in after Opara flicked on.
The Darlington goal was under seige in the closing minutes and four minutes of added time, but Patrick Collins led the resistance with Russell again delivering the goods with stops from Newton and Benjamin.