United went into the clash knowing that a victory would keep their hopes of promotion alive, but their top-six pursuit suffered a hiccup when Jon Taylor nodded the hosts ahead on five minutes.
However, a nine-minute brace from Conor Washington helped flip the game on its head, before Lloyd Isgrove pounced to double the advantage shortly before the half-hour mark.
Tom Bradshaw threw Salop the slimmest of lifelines in their survival bid by reducing the arrears shortly before the break, but Josh McQuoid pounced in the dying stages to seal the win for Posh and consign Michael Jackson's men to life in League Two next term.
In contrast, Notts County took a huge step toward preserving their League One status by beating nine-man Swindon Town 2-0 in a feisty affair at Meadow Lane.
Goals from Alan Sheehan and a late strike from Callum McGregor sent the Magpies five points clear of the relegation zone with one to play - third-from-bottom Carlisle United have a game in hand.