Bernard gave Everton a 19th-minute lead with a smart low finish. But Man Utd levelled six minutes later when Fernandes headed in from Luke Shaw’s cross.
Lucas Digne hit a post before Fernandes put United in front on 32 minutes with a cross that eluded Marcus Rashford but went in off the far post.
Everton pushed hard for an equaliser but Harry Maguire denied Dominic Calvert-Lewin before Abdoulaye Doucoure shot over.
Man Utd substitute Edinson Cavani sealed victory on the counter in stoppage time with his first Premier League goal, sweeping home after Fernandes’ pass.
A third straight defeat leaves Everton sixth, three points ahead of United in 14th.
Budweiser King of the Match: Bruno Fernandes (MUN)
Everton: 21 Nov v Fulham (A)
Man Utd: 21 Nov v West Brom (H)