The 19-year-old midfielder, who scored with his first touch on his professional debut in last weekend's 2-1 win over Brentford, provided an assist for David Wagner's side who got the better of Rafa Benitez's Newcastle United with a 2-1 triumph at St James' Park.
Nahki Wells gave Huddersfield the lead with a lovely sweeping finish from Rajiv van la Parra's dangerous cross on the stroke of half-time before Dwight Gayle levelled for the Magpies on the hour-mark when heading home after Danny Ward, on loan from Liverpool, had done well to keep out his initial penalty.
Against the odds, Huddersfield edged the Championship favourites with an 82nd-minute winner through Jack Payne which was made possible by a neat Palmer pass.
Palmer, who had earlier replaced Wells on 64 minutes, took possession in midfield before providing a lovely ball which invited summer signing Payne to advance into the area and finish expertly across Toon keeper Matz Sels.
Ward, in his second league start for the Terriers, did well to deny Jonjo Shelvey's first-half free-kick before keeping out Gayle's spot-kick but it was ultimately the contribution of Chelsea youngster Palmer which helped the West Yorkshire outfit secure their second straight win of the Championship campaign.
Check out the highlights below courtesy of HTAFC's official YouTube channel: