Roberto De Zerbi’s Brighton dominated possession, with United content to sit back and try to exploit Rashford and Antony’s pace.
Brighton goalkeeper Robert Sanchez beat away Fernandes’ effort in United’s first meaningful attempt on goal.
Crowds of Brighton fans were eager to play on De Gea’s nerves whenever the ball fell at his feet after a nightmare game for the Spaniard in Seville.
United, unhappy for a long time, created a flurry of chances shortly before half-time, with Fernandes, Anthony Martial and Christian Eriksen failing to convert.
Brighton quickly got off the blocks at the start of the second half. Ankiso forced De Gea to make a smart save before former United forward Danny Welbeck headed in from the resulting corner.
But neither side could break the impasse and referee Craig Pawson blew for extra time.