The harsh foul that the United defender committed on Kaoru Mitoma early in the first half resulted in Holgate’s dismissal.
Brighton took advantage of Holgate’s departure with goals from Danny Welbeck and Facundo Buonanotte in quick succession.
Simon Adingra’s late brace and Jack Robinson’s own goal in the second half condemned the woeful Blades to their sixth league loss in the previous nine games.
With 13 games remaining, Chris Wilder’s club is sitting seven points outside of safety and unlikely to make an instant return to the championship.
Sheffield has given up the most goals in their first 25 Premier League games this season—65—more than any other team.Within two minutes, James McAtee found Jayden Bogle on the edge of the area, and Bart Verbruggen blocked his effort, giving Sheffield a goal threat.
That turned out to be a pivotal moment as Brighton grabbed charge.
In the thirteenth minute, Holgate’s studs-up high challenge left Mitoma writhing in agony, cutting Wilder’s team down to ten men.
Referee Stuart Attwell first issued a booking for Holgate, but after reviewing the play using the pitchside monitor, he upgraded it to a red card.