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Two penalties from captain Paul Wotton, either side of Arturo Lupoli's sixth goal for Derby, and a nerve-settling third from Dutch defender Marcel Seip saw the Pilgrims win an incident-packed match.
They did so the hard way too, playing almost the whole of the second half without French central defender Mathias Doumbe who was controversially sent off for two yellow cards.
They were also reduced to nine men for several desperate minutes when substitute Hasney Aljofree was sidelined a broken nose.
Wotton netted his first spot-kick two minutes before the break after Sylvan Ebanks-Blake was clipped by Mo Camara following Hungarian playmaker Akos Buzsaky's delicate chip into the penalty area.
The lead lasted barely a minute before Lupoli, on loan from Arsenal, stretched to turn home a mis-hit shot by Michael Johnson with the Argyle defence appealing in vain for offside.
Replays showed referee Paul Taylor was correct in awarding that decision, but the same cameras showed he was wrong to dismiss Doumbe after the Frenchman tackled Morten Bisgaard to earn his second yellow card.
Taylor was centre stage just after the hour when Johnson tripped Barry Hayles on the edge of the penalty area to allow Wotton to send a second thumping kick past Lee Grant.
The goal seemed to knock the stuffing out of Derby, who never threatened the goal after keeper Luke McCormick denied Adam Bolder an equaliser with a twisting save.
Seip's second successive home goal 13 minutes from time was no more than outnumbered Argyle deserved for taking the match to their opponents.