Rovers dominated a one-sided South Yorkshire derby clash, but the Blades hit back with two goals in the last 10 minutes after Saunders' side had striker Billy Paynter sent off.
Paynter had given Doncaster the lead from the penalty spot in the 18th minute after visiting goalkeeper George Long had brought down David Syers, who made it 2-0 with a 63rd-minute header from David Cotterill's free-kick.
Rovers looked to be well in control until the Blades pulled a goal back with a controversial penalty converted by Nick Blackman after Joe Ironside had been judged to have been brought down by Andy Griffin in the 80th minute.
Paynter was sent off seven minutes later after tangling with Tony McMahon and Dave Kitson grabbed the equaliser in stoppage time.
Wilson, whose side remain above Doncaster in the table and in second position, said: "We had to dig deep and show our character.
"We started to put them under pressure in the second half, but it was only when we were 2-0 down that we did that. We got up a head of steam and when we do that we know that teams can't handle us. Once we scored the first goal I always thought we would get another.
"In my opinion I thought they were both stonewall penalties and maybe they thought they had the game won. But I thought we had a foothold in the game even before the sending off, which I can't comment on because I didn't see the incident.
"To get something out of the game is a great boost for us because this is a tough place to come.
"Doncaster have been doing well, but we showed our credentials. It's a great point from our perspective, but psychologically for them it will feel like a loss."