County started brightly, prompted by Adam Chapman in midfield, with former Pilgrims striker Chris Zebroski firing an early warning shot.
Conor Washington was first to test home keeper Luke McCormick as the visitors surged forward on 16 minutes.
Argyle countered through Lewis Alessandra on 32 minutes, forcing County keeper Lenny Pidgeley to make a double save as the home winger followed up on his first effort.
McCormick had to keep out a Washington angled shot on 43 minutes after the County winger was sent away down the right by Chapman's incisive, defence-splitting pass from the centre circle.
Washington fired just over at the start of the second half as County continued to make the most of their superior possession.
Ismail Yakubu looked set to convert from close range after a fine cross from Ryan Jackson, which acted as a spur for the home side, with danger man Alessandra firing high and wide when well placed.