Midfielder Steve Thomas settled a hard fought tie with a free-kick in off the bar when the game seemed set to go into extra time.
Both sides had near misses in the first half as Wrexhams Lee Trundle, Lee Jones and Jim Whitley shot wide and Huddersfield's Jon Stead shot over from three yards.
Steve Roberts broke the deadlock with a superb volley from a Darren Ferguson corner to give Wrexham the lead before Dwayne Mattis levelled for the Terriers in a goalmouth scramble.
Trundle shot over from close range and Martin Smith fired a shot against Wrexham's crossbar before Thomas settled it