County took a 14th-minute lead when Jack Diamond cut through the Argyle defence and let fly as he cut into the box.
Diamond's goal-bound shot took a late deflection off Matty Sorinola, past diving keeper Murphy Cooper.
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Playmaker Diamond also played a big part in County's 26th-minute second goal, crossing from the right for Harry Wood to force a brilliant save from Cooper, who could not hold the ball. Stockport striker Kyle Wootton was on hand to tap in.
Cooper made a good save with his feet to deny Wootton from close range in the 36th minute and player of the match Diamond fired just over from 20 yards just before half-time.
Diamond teed up Ryan Glover to make it 3-0 in the 49th minute after the County winger cut in, beat Alex Hartridge and fired home from just inside the box.
Substitute Xavier Amaechi gave Argyle some late consolation with a clinical 79th-minute strike from the edge of the box as County failed to clear a corner.
