Some sloppy defending gifted Argyle their goals and the home side were hit by a 30th minute injury to striker Svetoslav Todorov, restored to the team for the game, who was carried off with a knee problem.
Premiership referee Rob Styles, making a rare visit to the Championship, was the centre of controversy as he booked ten players and angered both sets of supporters with his decisions.
Charlton created enough chances to have won the game but squandered the best of them and also found Plymouth goalkeeper Luke McCormick in fine form.
In the end the home side run out of ideas and the defeat dropped them out of the top six in the Table.
Charlton fell behind as early as the fifth minute when a left-wing cross from David Norris wasn't cleared and Sylvan Ebanks-Blake scored from close range.
Charlton equalised six minutes later when a 25-yard shot from Danny Mills was pushed on to the post by McCormick and the ball rebounded off of the goalkeeper into the net for an own goal.
But the Plymouth keeper made amends with some fine saves, keeping out close range efforts from Luke Varney and Chris Iwelumo. Charlton's big striker also headed wide in the second-half from a simple chance.
Plymouth rarely showed any attacking intentions in the second-half but they defended well enough against a frustrated Charlton attack to keep the home side at bay.
The Pilgrims took three points back to the West Country, whilst Charlton's early season success has come to a stuttering halt.