The Terriers saw Keith Southern dismissed in the first half at The Valley on Saturday and fell behind to Rob Hulse's effort after 60 minutes.
But Simon Grayson's men are made of stern stuff and they hit back with two minutes to play as Clayton kept his cool to net his first goal in 12 matches.
Boss Chris Powell handed Arsenal loanee Emmanuel Frimpong his Addicks debut, while the visitors lined up without the attacking trio of Jermaine Beckford, James Vaughan and Sean Scannell.
Huddersfield spurned a glorious chance to open the scoring inside the opening two minutes. Clayton's shot was cleared off the line and the loose ball fell kindly for Peter Clarke but the defender, without a goal in 47 games, skied his effort over the bar.
Terriers defender Paul Dixon picked up a booking midway through the first half when he brought down Bradley Pritchard, but Johnnie Jackson's subsequent free-kick was punched clear by Alex Smithies.
Referee Lee Collins produced another card 10 minutes later, but this time a red one for Southern as he arrived second to the ball and ended up sliding through Michael Morrison in the middle of the pitch.
With their numerical advantage, Charlton's threat was bound to increase and some neat footwork from Ricardo Fuller opened up a chance for him to shoot late in the first half, but he dragged his effort wide.
Hulse headed over on the hour mark from Chris Solly's cross but made amends shortly after when he opened the scoring. Pritchard whipped in a cross from the right and Hulse was on hand to turn home from close range.
Frimpong's impressive debut was curtailed after 66 minutes as he appeared to tweak a muscle when testing Smithies with a well-struck shot.
Grayson summoned Alan Lee from the bench for the final 13 minutes and he was one of a host of Terriers players appealing for a handball against Salim Kerkar in the box, but Collins waved play on.
There was a different outcome in the 88th minute when Solly went to clear a cross but caught Clarke late and the ref pointed to the spot. Clayton stepped up and drove a powerful penalty past Ben Hamer to deny Charlton their fourth win on the bounce.
The visitors had Smithies to thank for preserving their point as he somehow kept out Hulse's effort from point-blank range.