The centre-back's mistake helped the visitors move into a two-goal lead but the division's bottom club hit back with a dramatic fightback.
Michael Tonge gave the Blades the lead deep into first-half stoppage time. Tonge outpaced Robbie Stockdale down the left, cut inside and as Mike Pollitt came off his line, clipped an angled shot past the keeper.
Earlier Pollitt had been the hero as he denied Neil Warnock's men with a tremendous double stop.
Andy Liddell smashed a curling, dipping 25-yard free-kick that the Sheffield United fans behind the goal were already celebrating as Pollitt somehow turned the shot over the bar.
From the resulting corner Liddell snapped up a clearance, darted into the area and crashed in a shot from five yards that Pollitt again saved.
Rotherham were dealt a body blow nine minutes before half-time when striker Martin Butler raced forward in an attempt to latch on to Paul McLaren's throughball but clashed with Blades keeper Ian Bennett, who was in for the suspended Paddy Kenny.
Bennett, on loan from Birmingham City, was making his debut and came out of his area to head clear. Butler was knocked unconscious as he was clattered and had to be stretchered off.
Andy Gray should have given the visitors the lead but mishit his shot from Paul Shaw's cross and his second attempt was blocked.
But seconds before the half-time whistle Tonge pounced to claim the lead.
A dreadful blunder by Rotherham skipper McIntosh two minutes into the second half gave the Blades a helping hand.
The centre-back under-hit his back-pass and Gray pounced to lash an angled drive towards goal. Pollitt parried the effort but Paul Shaw, who scored two for Rotherham in a loan spell at Millmoor at the start of the season, tucked away a simple chance.
Moments later it could have been worse for the home side when Alan Quinn crossed for Gray to head towards goal but Pollitt saved well.
But the home side pulled one back in the 54th minute when McLaren swung a free-kick into the area and Chris Swailes met it with a glancing header to beat Bennett.
And 20 minutes from the end McIntosh headed Rotherham level from McLaren's corner.