The former Barnsley midfielder's strike 13 minutes from time cancelled out Tommy Elphick's first senior goal for Brighton three minutes earlier.
A drab game at the Withdean Stadium only came to life with the late goals and straight red cards for Brighton substitute Gary Hart and Huddersfield midfielder Chris Brandon for a clash deep into stoppage time.
Brighton, with only one win from the previous six matches, had the better of a dull first half without causing the Huddersfield defence many alarms in open play.
The best efforts from the home side came from set pieces delivered by Dean Cox.
Elphick almost scrambled them in front from an early free-kick by the little playmaker and another free-kick from Cox was half volleyed into the side netting by Frenchman David Martot.
Huddersfield almost took the lead against the run of play, first when Brandon's fierce angled drive was deflected for a corner and then when top scorer Luke Beckett scuffed his shot on the stroke of half time.
Brighton, with former Falkirk captain Steve Thomson making an accomplished debut in midfield, improved after the break.
Leading marksman Nicky Forster, captaining the team with Dean Hammond suspended and Guy Butters on the bench after injury, was denied when Huddersfield keeper Matt Glennon smothered at his feet.
Glennon also foiled Cox, blocking his shot for a corner with his legs following a one-two with Alex Revell.
The deadlock finally ended when Elphick rose the highest to head in a Cox corner.
Brighton's joy was shortlived as Williams curled a free-kick around the defensive wall and into the top corner from outside the box.
Hart, brought on in place of Revell with four minutes left, saw red with Brandon following an ugly confrontation as Huddersfield worked a short corner.
The feud continued at the end of the match and they had to be separated by team-mates as the players headed for the dressing rooms.