Defeat sent Posh plunging into the relegation zone and left manager Darren Ferguson with plenty of food for thought.
Jamie Mackie broke the deadlock when leaving defender Craig Morgan trailing and firing past Joe Lewis in the 63rd minute and the points were in the bag when Rory Fallon rose high to meet a classy 69th minute Jim Paterson cross from the left.
Ferguson handed a debut to loan capture Danny Rose despite the teenage midfield man only arriving from Tottenham Hotspur in mid-afternoon.
Rose made an instant impression with some classy contributions in the opening period. He released Craig Mackail-Smith whose 11th minute shot came close to beating Plymouth keeper Romain Larrieu.
Mackail-Smith had the ball in the net just after the half-hour when pouncing on a rebound after Larrieu had spilled a Charlie Lee shot, but his celebrations were cut short by the flag of an assistant referee.
Plymouth were rarely seen as an attacking force but Darcy Blake was only denied by a fine save from Joe Lewis after a lung-busting length-of-the-field burst.
George Boyd became the second Posh player to see a 'goal' disallowed early in the second half before things turned miserable for the home side.
Day was stretchered off after being involved in a crunching challenge before Argyle struck at the other end.
Craig Mackail-Smith pulled one back for Posh four minutes from time, but it proved too little, too late.