United's away day troubles continued, despite taking the leading in Saturday's South Yorkshire derby at Rotherham.
Jose Baxter's first goal for the Blades secured a half-time lead but the Millers hit back after the interval with goals from Kieran Agard, Daniel Nardiello (penalty) and Rob Milsom.
New co-owner HRH Prince Abdullah bin Mosaad bin Abdulaziz Al Saud was part of the 2,536 Blades fans inside the New York Stadium.
Manager Weir made three changes from last week's league encounter. Howard, Porter and Cuvelier were handed starts with Long on international duty, Murphy injured and Taylor dropping to the bench, where he was joined by fellow striker Bunn, signed on loan from Manchester City on transfer deadline day.
The Blades were inches from making the perfect start. Just three minutes had elapsed when Morgan fouled Cuvelier and McMahon's 20-yard free-kick cannoned off the crossbar. Additionally, there were two penalty shouts as the ball dropped into the danger area off the woodwork when the ball appeared to hit the hand of former United defender Davis and Baxter was held back as he looked to latch on.
The home side won the game's first corner as a result of Howard racing from his own line but the goalkeeper saved comfortably on ten minutes when Frecklington burst through the back four but ran out of steam.
Another Blades penalty appeal was waved away when Davis clumsily brought down Porter, who, moments later was denied by Shearer rushing from his goal. Milson headed over a cross from Frecklington but with the next serious attack, the visitors opened the scoring. A right-wing throw-in saw BAXTER lose Mills and then poke through Shearer from an acute angle, in front of the Millers fans.
Despite Revell looking dangerous in the air, the Blades defence protected goalkeeper Howard well and the Blades went into the break with a deserved slender advantage.
Rotherham made positive change at the break, introducing a striker for a defender, and they created a chance within two minutes of the restart when Pringle's cross found Revell but he was crowded out by a covering challenge from Collins.
The Millers, however, were soon level. AGARD chanced his arm with a powerful shot from the edge of the box, which beat Howard.
Weir's team worked hard to immediately get back on top and, as in previous games, saw a lot of the ball. McMahon's cross evaded both Baxter and Flynn before the Blades made a positive double change - Taylor and debutant Bunn replacing Porter and Flynn.
There was more pain for the Blades, though, as Rotherham edged in front on 72 minutes, courtesy of penalty. McMahon was adjudged to have fouled NARDIELLO, who stepped up and powered home the spot-kick, to Howard's left.
And that wasn't it. With their next attack, Rotherham added a third. This time Maguire gave away possession and Revell held onto the ball long enough to lay off to MILSOM, who placed his shot into the bottom corner, via a post.
In the final ten minutes Howard saved from Pringle and Agard and to cap a miserable afternoon, McMahon and Bunn picked up late bookings.
Rotherham: Shearer, Brindley, Skarz, Davis, Mills, Frecklington, Revell, Milsom, Pringle, Morgan (Nardiello 45), Agard.
Unused: Hylton, Tubbs, Collin, Tidser, Rowe.
Blades: Howard, Maguire, Hill, Flynn (Bunn 69), Doyle, Porter (Taylor 69), Baxter, Collins, Cuvelier, Coady, McMahon.
Unused: Westlake, McGinn, Ironside, McFadzean, Willis.