First-half goals from Stephen Quinn and Ched Evans put the hosts in the driving seat, but late goals from Chris O'Grady and Gary Madine saw the League One game finish all-square.
Quinn opened the scoring in the 11th minute, seizing on a rebound to fire home after Evans' low shot had been deflected on to a post.
O'Grady wasted a gilt-edged chance to equalise, hitting the post from close-range after Blades goalkeeper Steve Simonsen spilled the ball.
The miss proved costly as Evans put United 2-0 up just a minute later, beating Owls goalkeeper Stephen Bywater with a near-post header from Williamson's cross.
As Wednesday pressed, James O'Connor steered a free header off-target and Ben Marshall twice threatened, but in a pulsating finish O'Grady (83) pulled a goal back for the Owls with a far post header and then Madine (86) headed the equaliser after beating Simonsen to a high ball played into the area.
Wednesday are third in the table after 13 games, two points behind leaders Charlton. The Blades are five points behind the Owls in seventh, having played a game less.