The Bluebirds enjoyed the better of the first half and were rewarded in the 45th minute as Jay Bothroyd opened the scoring with a thunderous 25-yard drive.
But United improved after the interval and equalised when Stephen Quinn bundled home from close range with 23 minutes remaining.
Cardiff almost snatched a winner late on as substitute Michael Chopra struck the crossbar, but the scores remained level.
Dave Jones' side stay sixth in the table, five points ahead of nearest rivals Blackpool and United, who move up a place to eighth.
Tony Capaldi replaced the injured Mark Kennedy in Cardiff's starting line-up, while Kelvin Etuhu was handed a place on the bench following his recovery from ankle problems.
United were only able to name six substitutes due to their extensive injury list.
Blades boss Kevin Blackwell made three changes to his starting XI, with Andy Taylor, Kyle Bartley and Glen Little coming in for Marcel Seip, Mark Yeates and Henri Camara.
Cardiff started brightly and Bothroyd went close in the second minute with a powerful shot on the run.
Steve Simonsen was then called into action to keep out free-kicks from Ross McCormack and Bothroyd, before Peter Whittingham forced the Blades goalkeeper into a fine save with a well-struck volley.
Bothroyd shot weakly at Simonsen when well positioned as the hosts continued to create chances at will early on.
But United weathered the storm and Glen Little tested David Marshall in the 18th minute with a shot from the edge of the area.
A lengthy lull in proceedings ensued thereafter, but when the next effort on goal did finally arrive on the stroke of half-time, it resulted in Cardiff taking the lead as Bothroyd capitalised on some defensive uncertainty by lashing home a left-footed shot from 25 yards.
United made a more encouraging start to the second period and James Harper saw a long-range effort fly over in the 53rd minute.
Cardiff winger Chris Burke then warmed the palms of Simonsen from 20 yards before Bothroyd went down in the penalty area, only to be booked for simulation by referee Danny McDermid.
United equalised in the 67th minute, Quinn eventually prodding home after Marshall had parried away a right-wing cross.
Cardiff responded superbly and McCormack saw a header cleared off the line within seconds of the restart.
With action now switching from end to end, Blades midfielder Yeates fired a shot straight at Marshall from 25 yards, before Cardiff's Gavin Rae saw a close-range effort pouched by Simonsen.
Burke blasted a shot over as the hosts piled forward for a winner in the closing stages.
Chopra, on as a late substitute, almost provided it with five minutes remaining, but his left-footed strike bounced back off the bar with Simonsen beaten.