Two goals from Jamal Salawu, either side of Angel Waruih's effort, were enough to see Argyle beyond their south-coast rivals.
Darren Way's youngsters appear to have turned the corner after a difficult run of form, putting in their second impressive performance in a four-day period, securing another deserved result.
Argyle opened the scoring on 10 minutes as Salawu's superb first-time shot flew into the goal from the edge of the Pompey area.
It was not until the hour mark that Argyle's pressure finally told again, when Waruih's first touch sent his marker the wrong way, before the midfielder fired into the net from 20 yards.
A third followed 15 minutes from time as substitute Rhys Shirley put through Salawu, who calmly slotted the ball past the advancing goalkeeper.
The only blot on an otherwise faultless performance came when Ethan Mitchell's innocuous challenge gave Pompey a soft penalty, which they converted for a consolation.
Argyle: Tyler Coombes, Oscar Halls (Ali Mansaray 82), Ethan Mitchell, Brandon Pursall, Oscar Rutherford (Charlie Miller 65), Carlo Garside, Trialist A (Trialist B half-time), Angel Waruih, Will Jenkins-Davies, Oscar Massey (Rhys Shirley 65), Jamal Salawu. Substitutes not used: James Morley, Jeremiah Medine.