Addicks winger Kyel Reid got to the byline and fired in a cross only for Huntingdon to miscue his clearance and, unchallenged, bundle the ball into his own net.
Soon afterwards, the hosts doubled their advantage. Akpo Sodje got between two defenders and guided Frazer Richardson's cross beyond Owain Fon Williams with his head.
The only surprise was that Charlton failed to add to their emphatic start, with captain Nicky Bailey inches away from meeting Lloyd Sam's cross. Sodje had a great chance to get his second goal of the game after Fon Williams failed to collect a cross but he volleyed wide with the keeper stranded.
Stockport had few chances but should have pulled a goal back when Jabo Ibehre shot wide with just the keeper to beat.
Fon Williams managed to keep the score at 2-0 late on when substitute Deon Burton hit a fierce drive from just inside the box only for the keeper to make a fantastic one-handed save and then smother the ball.