The visitors had John Lundstram sent off for upending Joel Veltman in a reckless challenge in the first-half, with the referee changing his decision from a yellow card to a red following a VAR review.
Despite Brighton's domination, United took the lead when league debutant Jayden Bogle made an impact after coming on as a second-half substitute.
Brighton substitute Danny Welbeck equalised three minutes from time from a set-piece when the ball fell to him in the six-yard box and the unmarked striker controlled it with his chest before firing a volley into the back of the net.
Brighton nearly scored the winner in stoppage time when Welbeck's header was cleared off the line and Alireza Jahanbakhsh's effort struck the woodwork.
Brighton stayed 16th in the standings while Sheffield United remained rooted to the foot of the table with two points from 14 games.