Stockport had a wretched day in Devon as the home side ended a run of seven home games without a win in emphatic style.
They lost keeper Alan Blayney just before the match after he broke a finger in the warm-up, had skipper Dave Challinor sent off midway through the first half and to top it all, defender Jim Goodwin scored two own goals.
Goodwin netted Argye's first and fourth goals in the sixth and 60th minutes. His first was negated by the match's third own goal by Plymouth skipper Paul Wotton but that was County's only bright spot of a disastrous day.
They were level only briefly, Marino Keith putting Argyle back in front in the 13th minute with a far-post header.
Challinor was dismissed in the 28th minute, handling David Friio's throughball to Keith and being harshly adjudged to have prevented a goalscoring opportunity.
Challinor is now set to miss the FA Cup second round game between the two sides at Edgeley Park in a fortnight's time although County manager Carlton Palmer revealed afterwards that referee Mark Warren had agreed to review this decision.
Argyle rubbed salt in the visitors' wounds three minutes before half time when midfielder Steve Adams headed home Lee Hodges' left-wing corner.
Stockport introduced all three of their substitutes before the hour but the changes did little to stem the green tide.
Goodwin's second own goal on the hour, when a goalline clearance rebounded off his shin into the net, left County with an impossible task and, in truth, they were lucky not to concede more.
Plymouth striker Micky Evans, who was a constant menace to County's defence, came closest to adding another goal when his header from Wotton's cross forced Lee Jones into a save