Not even a hat-trick from Leon Clarke, which took the Blades' striker to the top of the league's goalscoring charts, was enough to prevent them coming off worse in the nine-goal classic at Bramall Lane.
Clarke scored his 12th goal of the season in a lengthy period of injury time to give the home side a glimpse of narrowing the gap on leaders Wolverhampton Wanderers after they had pulled back from 5-2 down with just five minutes left.
Yet it was another hat-trick from Fulham's much-touted 17-year-old England youth international Ryan Sessegnon that ultimately saw the Londoners home.
It meant Chris Wilder's United remained on 36 points, still two behind Wolves, who host Leeds United on Wednesday.
Cardiff City moved to within a point of the leaders and leapfrogged Sheffield United thanks to a hard-earned 1-0 win at Barnsley, secured by an 83rd-minute winner from Callum Paterson, his first goal for the club.
Chris Coleman's debut as manager of Sunderland ended in familiar disappointment for the Championship's bottom club as they lost 2-1 at Aston Villa.
Coleman left his position as Wales manager on Friday to take on the job at one of England's ailing giants, who have won just once this season, but his appointment signalled no immediate change of fortune.
Albert Adomah and Josh Onomah scored for Villa to enable them to move up to fourth in the table on 32 points while Lewis Grabban's 10th goal of the season in reply at least gave Coleman a glimmer of hope for the future.
Villa also leapfrogged Bristol City, who lost 2-1 at home to Preston North End, in the playoff zone.
(Reporting by Ian Chadband; Editing by Toby Davis)
