Wednesday led through Darren Potter, but Williamson levelled with a second-half free-kick.
United were denied an early lead after ten frantic minutes when the upright saved their cross-city rivals.
A corner driven in by James Harper was met by Darius Henderson, but his badly aimed header cannoned off Owls skipper Darren Purse and smacked against the post.
Twice Jermaine Johnson was involved as Wednesday threatened on the break after the visitors hogged possession.
Johnson slipped a clever pass for Luke Varney, but he fired wide and then a cross was met with a Varney header.
An accurate clearance by keeper Steve Simonsen was headed on by Henderson and strike partner Richard Cresswell beat Mark Beevers, but angled his shot just wide.
Ex-Wednesday striker Cresswell went off with blood pouring from his face after 35 minutes following claims he was elbowed by Johnson.
With United down to ten men Wednesday cashed in the advantage and grabbed the lead five minutes from half-time when Varney's cross from the left was met by Potter, whose sidefoot volley gave Simonsen no chance seconds before Cresswell returned with his head bandaged.
Seconds before the break Wednesday went close again when Tommy Spurr's corner was met by Beevers, but he glanced a header wide.
On the hour United equalised after Eddie Nolan was booked for cutting down Stephen Quinn as the midfielder darted past him.
Williamson curled in the free-kick from 20 yards over keeper Lee Grant who drifted too far forward as the ball looped in off the post.
A deep cross from Cresswell found Henderson in the area, but his header failed to trouble Grant and when Henri Camara raced into the box, his shot hit the post and his follow-up from the rebound did the same.
United were appealing for a penalty with 12 minutes to go when Camara went down under a challenge from Purse, but the ref waived away the claims.
Twice Varney went close to a late Wednesday winner, but he was denied by Simonsen and with seconds to go Johnson blazed over from close range.