Birmingham City leapfrogged Burton Albion with a 1-0 home win over Nottingham Forest on Saturday and sent the Brewers into the Championship's bottom three.
Che Adams' fifth-minute strike was enough to send the Blues to their fourth win of the campaign and push them on to 15 points from 17 games.
That leaves them two points above Albion, who now sit 22nd in the table.
They are one point and one place better off than Bolton Wanderers, who extended their unbeaten run to six games with a goalless draw at Preston North End on Friday night.
Meanwhile, Sunderland remain bottom of the division after a 2-2 home draw with Millwall - a result that sees the Black Cats claim an unwanted record.
With George Saville's double ensuring a share of the spoils for the Lions, despite goals from Lewis Grabban and Adam Matthews, Sunderland became the first team in English football history to fail to win in 20 successive home games.
The Black Cats are Burton's next opponents at the Pirelli Stadium on Saturday, following the midweek fixtures, when they are likely to have new boss Chris Coleman in the dugout.
Brentford will head into Tuesday's clash with the Brewers at Griffin Park on the back of defeat as they were beaten 2-0 by Cardiff City.
Joe Ralls and Danny Ward both struck before the Break to ensure the Bees' longest-ever unbeaten run in the Championship came to an end.
Burton Albion 1 - 3 Sheffield United
Elsewhere in the second tier, Wolverhampton Wanderers moved back above Sheffield United at the summit thanks to a 2-0 win at Reading, courtesy of goals from Ivan Cavaleiro and Matt Doherty, while Derby County drew 1-1 at Fulham in the late kick-off on Saturday.
Matej Vydra secured the point for the Rams as he canceled out Oliver Norwood's opener.
