Albion forward Welbeck volleyed home three minutes from time as the beleaguered Blades had to settle for only a second point of a miserable campaign at the end of their 14th fixture.
Jayden Bogle’s deflected second-half strike on his top-flight debut had put the visitors on course for an unlikely victory after John Lundstram’s dismissal left them with 10 men for 50 minutes.
Chris Wilder’s battling side could even have ended a tense contest empty handed as Alireza Jahanbakhsh headed against the crossbar deep into added time.
United sit eight points from safety after ending an eight-game losing streak, while Brighton move two points above the relegation zone as their alarming home form continued.
The Seagulls, backed by 2,000 fans on Sunday afternoon, have now won just one of 16 top-flight fixtures at the Amex Stadium in 2020.
Defiant Blades boss Wilder insisted ahead of the game he would only walk away from his job if he felt it was in the best interests of the club he has guided from League One to the top flight.
He responded to Thursday’s 3-2 home loss to Manchester United by recalling goalless club-record signing Rhian Brewster and handing midfielder Lundstram his 100th Blades appearance.
In front of a smattering of socially-distanced supporters, both sides struggled to threaten during a first half in which Brighton controlled possession.
United’s first meaningful attempt came 10 minutes before the break when David McGoldrick – scorer of both goals against United – saw a 20-yard free-kick touched wide by Seagulls goalkeeper Robert Sanchez.
The visitors were enjoying their best spell of the game at that stage before the premature end of Lundstram’s milestone appearance halted their momentum.
Referee Peter Bankes initially produced a yellow card when the midfielder overran the ball and lunged at Joel Veltman, before delighting the limited home crowd by upgrading the punishment to red having watched a replay of the incident on a pitchside monitor.
Holland international Veltman – playing in place of the injured Tariq Lamptey – did not return for the second half, with Jahanbakhsh brought on to give the hosts greater attacking threat.
Despite their numerical advantage, Albion were almost caught out on the counter-attack just before the hour mark.
Brighton continued to be camped in United’s half but failed to heed the earlier warning as they fell behind.
After McGoldrick was slipped in on the left, Bogle – a summer signing from Derby, who had replaced ineffectual £23.5million man Brewster – was on hand to drill home the cutback via a hefty touch off Adam Webster.
The goal increased the dissatisfaction among the restless home fans.
Webster tested Blades goalkeeper Ramsdale from distance and Connolly headed off target with the goal gaping, while Burke squandered an excellent chance to wrap up victory at the other end.
Burke’s miss became extremely costly minutes later.
Ramsdale had gone 17 games without a clean sheet – dating back to his days with former club Bournemouth – and he was once again left to pick the ball out of his net as Leandro Trossard’s ball into the box broke for Welbeck to chest down and smash home from inside the six-yard box.
The equaliser ensured United’s winless run since defeating Chelsea 3-0 in July would stretch to 17 league games.
It could have been worse for them in the dying moments but Jahanbakhsh could only nod against the frame of the goal during a frantic finish.