A pulsating Steel City derby at Shirecliffe ended with Troy Pennycooke-Morgan securing a share of the spoils for the Blades with virtually the last kick of the game.
Despite leading twice, including in the 89th minute, the Owls were unable to hang on, with Nathaniel Foster also on target for the Blades from the penalty spot.
The opening exchanges were typical of a local derby, although the Blades appeared more comfortable on the ball.
In came as something of a surprise when Wednesday took the lead after 17 minutes after a poor clearance was seized upon.
The home side responded quickly with the industrious Chappell causing the visitors problems with his pace and trickery.
Indeed, on the half-hour mark Chappell's lung bursting run was ended by a cynical challenge in the box, which allowed FOSTER to confidently level from the spot.
With Chief Executive Trevor Birch watching from the sidelines, United's youngsters continued to dictate the game with Chappell and Foster both coming within a whisker of giving the Blades the advantage.
After seeing a series of half-chances go begging, the Blades looked like getting caught by the sucker punch when the Owls took the lead in the latter stages following some indecision from a corner.
Despite the obvious setback, United responded immediately and PENNYCOOKE-MORGAN burst through Wednesday's backline before rifling the ball home to cue jubilant celebrations.
Coach Kevin Fogg was full of praise for his troops but felt their performance warranted all three points:
"It is disappointing not to get all three points because we certainly had enough chances, but I can't fault the lads for effort and character.
"Our problem all season has been scoring goals, although Troy deserves a lot of credit for the way he finished his chance under pressure."
Blades: Andrew, Brown, McFadzean, James, Darlow, Pomares, Gregory, Williams, Foster, Slew, Chappell (Pennycooke-Morgan 75).
Unused: O'Kane, Wilkinson, Lammy, Ahmadi.