The Owls, for whom Darren Potter opened the scoring on Sunday with a brilliant volley at the end of the first half, are one point from safety with two games remaining.
They would have been out of the bottom three with a win but Williamson curled a 60th-minute free-kick from near the goalline straight into the top corner to ensure another rip-roaring local derby ended all square in front of a Hillsborough crowd of 35,485.
Whether Williamson aimed for the top corner is arguable, but his fortuitous strike saved face for a Blades side that started the day 10 points adrift of the top six and had only pride to play for.
Both sides made one change, with Owls striker Leon Clarke replacing Tom Soares and the Blades opting for Williamson instead of Glen Little in midfield.
There were surprise recalls to the substitutes' bench for United strikers Henri Camara and Ched Evans, who have been struggling with groin and shoulder injuries respectively.
The Blades almost stole into an eighth-minute lead when Darius Henderson's header ricocheted off Eddie Nolan's knee and crashed against the post.
Luke Varney responded for the Owls with a low shot that was comfortably gathered by Blades goalkeeper Steve Simonsen, but otherwise neither side could eke out an opening in the first 25 minutes.
It was fast and furious and both Nolan and Varney required early treatment after thundering challenges, while Owls skipper Darren Purse reminded Stephen Quinn what was at stake with an early scything tackle.
Then on the half-hour mark Henderson's brilliant flicked header sent Richard Cresswell racing into the penalty area but the Blades striker pulled a low right-footed shot wide.
Cresswell was then felled by an errant elbow from Jermaine Johnson and was forced to leave the field for treatment before Owls defender Tommy Spurr's free header from Potter's free-kick flew over the crossbar.
Wednesday then capitalised on their numerical advantage to break the deadlock in the 41st minute.
Varney charged into the open space down the left and curled a fine cross into the path of Potter, who expertly volleyed the ball beyond Simonsen from 12 yards to send most of Hillsborough into a bouncing blue and white frenzy.
Camara, supposedly out for the rest of the season, replaced James Harper just after the interval, while Owls goalkeeper Grant held Quinn's low drive.
The Blades then levelled the scores with a lucky equaliser when Williamson's free-kick out near the corner flag curled beyond Owls goalkeeper Grant and inside the far post.
Simonsen then saved superbly at the other end to keep out Clarke's header and when Varney was clean through Blades skipper Chris Morgan timed his tackle to perfection to deny the Owls forward a shooting chance.
The Owls battled gamely to the end in search of a winner, with Johnson's thumping drive beaten clear by Grant and another effort from the Jamaica international in the dying moments flying high and wide.