The home side were denied a clear penalty for handball against Lee Peltier in the second minute of Tuesday night's League One clash at Victoria Road, but from then on the visitors dominated the first half.
Their reward finally came after 28 minutes when Joey Gudjonsson picked up a short corner and drilled a shot across goal, where Tom Clarke was on hand to poke home from close range.
A penalty was eventually given to the hosts after 58 minutes for handball against Peltier and Green confidently blasted the ball past Ian Bennett.
Huddersfield threw everything forward in the final moments in search of a winner and could have earned it on three occasions. However, goalkeeper Tony Roberts was equal to everything thrown at him.