Erik ten Hag named a unchanged starting XI from the one that secured victory against Fulham on the opening weekend, with Summer signing Matthijs de Ligt once again left on the bench.
Instead, Maguire partnered Lisandro Martinez in the centre of defence as the rain poured down at the Amex.
United looked the more likely of the two sides to get in front but it was Fabian Hurzeler's side that would ultimately seize the initiative before the end of the first-half.
Joao Pedro unleashed an enticing ball across the box from Brighton's right flank that Maguire failed to clear allowing Kaoru Mitoma to collect inside the box.
Harry Maguire could be seen responding to team-mates after Brighton took the lead on Saturday
The Japan international then slid a low cross into an onrushing Danny Welbeck who tapped home from close range against his former club to mark a century of career goals.
Immediately after the ball crossed the line TV cameras picked up an exasperated Maguire telling his team-mates: 'I couldn't get the ball.'
Maguire was almost caught out after the restart after Martinez stayed up the pitch and Brighton counter-attacked.
The England international was unable to stop James Milner getting a shot off at close range but Diogo Dalot rushed back to clear on the goalline to keep United in the game.
United would eventually find their way back into the game however, and Amad Diallo's deflected strike drew them level on the hour mark.
The visitors looked to have pulled in front through substitute Alejandro Garnacho's before a VAR check showed the ball struck Joshua Zirkzee before crossing the line.