Argyle's Joe Mason volleyed the visitors in front at the near post after just 54 seconds from Rory Patterson's by-line cross.
Plymouth's Curtis Nelson saw red after 11 minutes for being the last man when he hauled down Jordan Rhodes on the edge of the box.
Pilgrims boss Peter Reid was then sent to the stands, possibly for dissent when referee Paul Tierney stopped him coaching from the touchline following Nelson's dismissal.
Huddersfield then gifted Plymouth a second goal when Kevin Kilbane's loose free-kick handed possession to Patterson in the 14th minute. He put Mason in the clear and the striker scored his second of the night with a shot which went in off goalkeeper Alex Smithies as he advanced off his line.
Town roared back and hit three goals in 13 minutes midway through a breathless first half.
Plymouth's Kari Arnason scored an own goal after 19 minutes when he diverted Anthony Pilkington's cross into his own net.
Rhodes made it 2-2 with a sweet half-volley struck from 18 yards in the 29th minute and Clarke put the Terriers in front three minutes later, scrambling the ball home after Rhodes had a shot blocked on the line.
It got worse for Plymouth in the 53rd minute when Stephane Zubar was sent off for a second yellow. It is Plymouth's 10th red card of the season including Reid's dismissal.
To cap an extraordinary night, Plymouth's Mason received a standing ovation from home fans for his two-goal blast when he was substituted after 76 minutes.
Town fans then roundly booed their own team at the final whistle for struggling against nine men, even though they won.