A dire first half was made even more miserable after the break as City skipper Darren Purse was dismissed in the 70th minute following a challenge on Nick Chadwick.
Argyle skipper Paul Wotton dispatched the spot-kick and City's misery was completed by David Norris who ran through to double the score in the 81st minute.
City boss Dave Jones kept faith with the side held to a scoreless draw by Derby.
A mistake by Purse gave Jason Jarrett a second minute striker on goal, but his shot flew straight to Neil Alexander.
Despite only scoring seven goals in their previous 12 away outings, Argyle pushed forward with three up and looked the more dangerous in the early stages.
Norris brought a fine reflex save from Alexander in the 17th minute as the visitors continued to press forward.
Purse conceded a free-kick in a central position on the stroke of half-time, but City broke away quickly to force a Jason Koumas corner and a header from Michael Ricketts was tipped over by Romain Larrieu for the Pilgrims keeper's first action of the half.
The Bluebirds began the second half with Joe Ledley making a run down the left, but Ricketts' goal attempt was pushed behind for a corner.
The Bluebirds looked short of attacking options and fired endless long balls down into the Argyle half that were easily dealt with by the visitors defence.
Tony Capaldi rifled a first-time shot wide following a quick break out of defence just before Paul Parry was brought on by Jones in place of Kevin Cooper in the 65th minute.
Five minutes later Purse was dismissed after bringing down Nick Chadwick and Argyle skipper Wotton thundered the spot-kick into the corner of the net to give the visitors a deserved lead.
A Koumas free-kick in the 78th minute whistled past the post as ten0-man City tried to force their way back into the game.
But it was Argyle who went further ahead when Norris was left free on the right flank to collect a Micky Evans pass before shooting into the corner.
City huffed and puffed but never managed to look as though they could pull one back, let alone the two needed.