City made one change from the side that beat Watford, with Tony Capaldi taking over from the injured Mark Kennedy, while there was a welcome return to the bench for Kelvin Etuhu.
The Blades were missing a number of first-team players including Wales international Ched Evans.
Jay Bothroyd had the crowd on their feet straight from the kick-off when he strode through the middle before lashing a low shot just wide of the post.
Ross McCormack was the next to bear down on goal but he delayed his shot and the chance was lost.
By the 11th minute, Paul Connolly and Nyron Nosworthy had both received yellow cards as the United defence struggled to keep the Bluebirds at bay with Bothroyd, Peter Whittingham and McCormack all testing keeper Steve Simonsen.
Despite putting the visitors under pressure, City were unable to get the goal their superiority deserved until the 44th minute.
Paul Quinn released Chris Burke down the right flank and he passed inside to Bothroyd.
City's skipper turned on the ball and hammered a 20 yarder into the net with Simonsen rooted to the spot.
Darcy Blake was harshly booked five minutes into the second period after a challenge on Simonsen as City started where they left off and then Quinn was yellow-carded after hitting the referee with the ball after yet another free-kick was given against his side.
Bothroyd was shown the fifth yellow card of the evening in the 62nd minute for allegedly diving in the area. That was his 10th of the season and he will be suspended for the next two matches.
Totally against the run of play the Blades were level four minutes later when David Marshall pushed out a close range shot from substitute Mark Yeates only for Quinn to push home the loose ball.
Michael Chopra replaced McCormack in the 82nd minute and with his first strike on goal rapped the Blades crossbar, but that was the closest they came and they had to be content with a point.