Marino Keith, criticised by Plymouth manager Paul Sturrock in the wake of last week's reversal at Rushden, scored one goal and set up two to pile the pressure on Stockport manager Carlton Palmer.
Scotsman Keith opened the scoring midway through the first half and then set up Lee Hodges and Jason Bent for well-worked goals as Argyle knocked three goals past Ireland international goalkeeper Nick Colgan inside eight minutes Luke Beckett pulled one back for Stockport before the interval but Plymouth hung on to win the battle of the previously winless and kick-start their season.
Stockport welcomed back star striker Beckett, who missed last week's 2-1 home defeat by Luton with a stomach upset, and midfielders Ali Gibb and Aaron Lescott after injury but soon found the changes made no difference to their fortune.
Argyle's opener came from a five-man move which ended with Norris crossing into the box, where Tony Capaldi flicked on for Keith to fire home from close range.
Keith then set up Hodges by flicking on Paul Wotton's corner to the far post, where Hodges stole in, before laying a beautiful pass back to Canadian international Bent, who lashed the ball into the corner of Colgan's net from 25 yards.
Beckett seized on Graham Coughlan's error outside the Argyle penalty area and finished with the sort of strike that demonstrated why Sheffield Wednesday want to sign him, but, although Gibb went close immediately afterwards, County could find no way back in a second-half ruined by the poor refereeing of Eddie Ilderton.