On the evidence of this game the Rams are a long way off of securing a place in the play-offs while the Owls may just about secure their safety.
But it was the visitors who played with the greater urgency as their pitiable situation dictates as they took a 16th minute lead following a swift break down the left.
Michael Reddy escaped the attentions of Richard Jackson and his fierce cross-shot was slid home by the hapless Barton.
And the visitors were angered when referee Michael Ryan waved away a clear-cut penalty after Derby keeper Lee Grant flattened Lloyd Owusu as the striker ran clear on goal.
But in an act of almost criminal self-harm Barton saw red minutes later as he clipped the heels of striker Reddy as he too threatened to run clear on goal.
As the half-time whistle rescued the Rams from further torment it was difficult to see a route back into the game.
But when Georgi Kinkladze finally escaped the attentions of his marker he crossed from the left for sub Fabrizio Ravanelli to flick on and Adam Bolder volleyed home.
Incredibly the Rams took the lead on 70 minutes when Kinkladze fed Morris and his low cross was converted by Bolder at the far post.
Morris was then tripped by Gary Monk as a third goal was on the cards for the Rams and with the last throw of the dice conjured up an equaliser.
Monk's free-kick was headed down by Shefki Kuqi and fellow sub Tony Crane prodded home the equaliser.