Blackpool's relegation to League Two was confirmed as Peterborough came from behind with five second-half goals.
The Seasiders were playing in the Premier League as recently as 2010-11.
Blackpool needed a win to have any chance of avoiding a second successive relegation and grabbed an early lead through striker Jacob Blyth's header.
But a Jon Taylor hat-trick, Marcus Maddison's penalty and Shaquile Coulthirst's finish for Posh dashed any hope that Blackpool had of survival.
Their relegation from the Football League's third tier was also confirmed by a win for Lancashire neighbours Fleetwood at already-relegated Crewe.
Three relegations in five seasons makes Blackpool's drop from the first to the fourth tier of English football one of the quickest in Football League history.