But the latter was deemed to have handled Harry Maguire's goal-bound effort in the dying seconds and, although the full-time whistle had been blown, VAR inteverned and Fernandes calmly dispatched his ninth Premier League goal.
That was harsh on the Seagulls who had dominated for large spells and rattled the frame of the goal five times, but it was enough to get Solskjaer's men up and running in truly breath-taking fashion.
Solskjaer will have been pleased to see his side respond immediately to falling behind, while the visitors carried much more attacking threat in the second half. Rashford's clinical strike was also a thing of beauty and, crucially, United are off the mark.
The visitors were slow out of the blocks and found themselves on the back foot in a first half where Brighton were creating the better chances, and the Seagulls hit the woodwork five times in a contest that could have ended very differently.
Manager rating (out of 10)
Ole Gunnar Solskjaer, 5 -- The Norwegian recalled Aaron Wan-Bissaka, Nemanja Matic and Mason Greenwood but all had little effect. Whatever he said at half-time had the desired impact and his side started the second-half much sharper, but United paid the price for inviting late pressure.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
GK David De Gea, 5 -- He reacted well to tip Adam Webster's looping header on to the bar in the first half, but was relieved to see Brighton hit the frame of the goal so many times. Comfortably beaten by Maupay's ice-cool penalty, but later denied the same man with a smart save.
DF Aaron Wan-Bissaka 5 -- Returned to the team in place of Timothy Fosu-Mensah but for once his performance was lacking any explosive bursts of pace down the right. He did at least produce an important block to thwart March.
DF Victor Lindelof, 6 -- Had to be on his toes from the off, ensuring Brighton had to settle for a corner as Maupay's cross looked to hurt United early on. There have been questions raised over his capability to play at centre-back, but he was steady today.
DF Harry Maguire, 7 -- The United skipper won some important aerial battles and made a nuisance of himself, forcing Dunk to turn the ball into the back of his own net, while his last-gasp header set up the dramatic ending.
DF Luke Shaw, 6 -- Did his best to provide an outlet and offer attacking support down the left. The full-back produced nothing sensational but equally nothing calamitous in a steady display.
MF Nemanja Matic, 6 -- Encapsulated United's frustration perfectly when his careless outstretched arm caught Connolly, but his cut-back into a dangerous area drew the equaliser.
MF Bruno Fernandes, 8 -- Ugly, but effective. Some wayward passing and a cheap booking were followed by a careless collision with Tariq Lamptey in the box that gifted the hosts the lead. He redeemed himself with an inviting free kick that led to the equaliser and sent Rashford on his way with an excellent pass the ended in United taking the lead, before sealing all three points with another penalty -- although probably the only one that he'll score beyond the final whistle.
FW Mason Greenwood 5 -- Replaced Daniel James in the side. He could only drag an effort comfortably wide after a rare mistake from Lamptey before comfortably beating Mat Ryan with his next attempt, but United failed to beat the offside flag.
FW Anthony Martial, 6 -- The Frenchman was painfully close to connecting with Fernandes' in-swinging cross and he later showed excellent feet before feeding Rashford in behind. Much like United, he was relatively quiet, but he always carried a threat.
FW Marcus Rashford, 7 -- The England forward put a great chance on a plate for Mason Greenwood before netting himself moments after the restart, but on both occasions he had strayed offside. Redeemed himself with a simply exquisite run and finish that twice had Ben White on the floor.
MF Fred, 6 -- Brought on for Pogba to help steady the ship as Brighton searched for a leveller and conceded a free kick within seconds of entering the playing field.
DF Eric Bailly, NR -- Replaced Greenwood as the visitors looked to tighten things up. He put his body on the line for the cause, but it appeared in vain as Brighton snatched what they thought was a late equaliser.
MF Donny van de Beek, NR -- Replaced Martial late on but didn't have time to have an impact, although his low cross drew a late corner.