Centre-back Neill Collins headed the Blades level after 83 minutes from a Tony McMahon free-kick.
Danny Wilson's side seemed to be dead and buried after having a man sent off in each half. Skipper Michael Doyle was first to be sent off after just 15 minutes for his challenge on home striker Mike Grella, and he was followed by midfielder Ryan Flynn in the 72nd minute for his high challenge on Iron full-back Christian Ribeiro.
By then Scunthorpe looked to be heading for their first win of the season after a dream debut for striker Leon Clarke, who is on loan from Charlton. Clarke came off the bench in the 55th minute as part of a double substitution which saw fellow new signing Karl Hawley handed his debut.
And five minutes later Clarke was on the end of a ball into the box from Mark Duffy to plant his header into the bottom corner past goalkeeper Mark Howard. It was only Scunthorpe's second league goal of the season.
The Blades seemed out of luck when Collins rattled the woodwork after 66 minutes with a header from a free-kick. But his late strike rescued them a point and left the Iron still looking for their first win.