Things looked promising for the visitors when Jose Baxter gave them the lead eight minutes before half-time.
However Kieron Agard emphatically levelled six minutes into the second half, then Daniel Nardiello (penalty) and Robert Milsom netted in the space of three minutes to move Rotherham up to fourth and leave the Blades with just one win from their first six games.
Peterborough missed out on the chance to join Leyton Orient at the top as they were held to a 2-2 draw at Crewe.
It could have been worse for Darren Ferguson's side, as goals inside the first 21 minutes from Vadaine Oliver and Ajay Leitch-Smith had Crewe two goals up.
The hosts were made to pay at the end of each half, with Tyrone Barnett replying at the end of the first half and Michael Bostwick heading an injury-time equaliser.
Bradford moved above Brentford following an emphatic 4-0 win over the Bees at Valley Parade.
The visitors' cause was not helped when goalkeeper David Button was dismissed in the 26th minute and James Hanson made them pay when he got the opening goal four minutes before half-time.
Three goals in the space of nine second-half minutes from Nahki Wells, Garry Thompson and Hanson finished off the visitors as the Bantams moved up to fifth.
Crawley came from behind to sink Gillingham 3-2 and climb to sixth.
Danny Kedwell opened the scoring for the visitors from the penalty spot in the 47th minute to give the visitors the lead.
It was 10-a-side when the home side's Gary Lee and Gillingham's Charlie Lee were dismissed, then Kyle McFadzean (55) and Billy Clarke (66) turned things around.
Although Leon Legge levelled for the Gills in the 69th minute, Clarke's second of the game 12 minutes later won it for the hosts.
Alex Pritchard's superb free-kick was not enough to secure Swindon victory, as their match at MK Dons finished 1-1.
The Tottenham loanee's first league goal was one to remember from 25 yards out but Patrick Bamford equalised after racing clear shortly after the visitors' Nathan Byrne was sent off for the visitors for a stamp on Shaun Williams' foot.
Elsewhere, Tom Pope's last-minute goal gave Port Vale victory at winless Carlisle, while Tranmere and Stevenage ended goalless.