There was one change in the Swans line-up for their 100th League and Cup match at their new ground, with Joe Allen replacing the injured Mark Gower.
James Beattie went close for the visitors with a fourth-minute header following a long throw by Greg Halford as the Blades pinned Swansea back in the opening minutes.
Midway through the half a header by Darius Henderson sent Beattie through on goal but he lifted his shot high over the bar.
The visitors' goal was threatened in the 27th minute when Tom Butler cut inside to curl in a shot but Paddy Kenny watched carefully as it cleared the crossbar.
Stephen O'Halloran was stretchered off in the 36th minute after damaging his knee and was replaced by Alan Tate.
In an amazing start to the second half, Henderson was sent off after just 30 seconds by the referee after catching Angel Rangel in the face with an elbow.
Five minutes later, Kenny made a superb double save from Butler and then Jason Scotland as the Swans pressed home their advantage.
In the 53rd minute, they were awarded a penalty when Gary Naismith brought Scotland down on the edge of the area. Scotland stepped up to ram the spot-kick home himself to give the Swans the lead.
Butler then forced Kenny to make another superb stop after he had worked his way into the danger area.
Ten minutes from time Darren Pratley raced through only to stab his shot wide of the post with Kenny beaten.
The Swans were shocked in the 87th minute though when their defence failed to cut out a ball in the danger area and Blades skipper Chris Morgan ran in unopposed to lift the ball over Dorus de Vries for the equaliser.
Blades manager Blackwell immediately threw on Ugo Ehiogu to shore-up his defence and keep hold of the point they never really looked like gaining.