Paul Pogba then set up Fernandes, whose deflected shot found the corner to make it 2-0 on 29 minutes, during a first-half dominated by Man Utd.
The Seagulls pushed on after the break only for a lightning counterattack, started by Nemanja Matic, to end with Greenwood’s cross being volleyed in by the imperious Fernandes.
Aaron Connolly and Neal Maupay then forced fine saves from David De Gea, but the hosts find no reply.
Ole Gunnar Solkjaer’s side is back up to the fifth place with 49 points.
Brighton & Hove Albion are 15th, on 33 points, six above the relegation zone.