The Terriers won just once on the road as they were relegated from the Premier League last season, a 2-0 win at Wolves in November.
Their first trip of the season in the second tier looked like it would end in three points for manager Jan Siewert.
Karlan Grant added a his second goal of the season when he converted from the penalty spot on the stroke of half-time.
Grant Hall scored the equaliser in the 83rd minute to deny Huddersfield a win.
Charlton continue their perfect start to their Championship season despite being tipped for relegation.
They beat Stoke City 3-1 at home with Lyle Taylor and Chuks Aneke scoring either side of Tom Ince’s goal before Conor Gallagher sealed the three points with a late third.
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