Both sides struggled to create chances in a disappointing first half, although Plymouth keeper David Button produced a fine stop to prevent Scott Wagstaff firing the Addicks in front after 28 minutes.
Argyle's Kari Arnason saw a stunning 49th-minute volley go agonisingly over the bar, but it was Charlton who broke the deadlock six minutes later.
Marcel Seip, who was recently on loan at Charlton, made a poor backpass and Wagstaff capitalised on the error before placing a low shot beyond the reach of Button.
Seip produced a crucial clearance to prevent Joe Anyinsah's header doubling the advantage before Rory Patterson almost grabbed an equaliser with an overhead kick which was well saved by Rob Elliot.
Charlton made the game safe in the 90th minute when on-loan Liverpool striker Nathan Eccleston's run into the box ended with a low shot past Button.