Bernard gave Everton the lead early in the game, after latching on to a flicked header from Dominic Calvert-Lewin, before finishing past David de Gea.
Everton's lead didn't last long though, as Fernandes equalised with a superb header off a Luke Shaw cross. Fernandes then put United ahead a few minutes later, with a cross meant for Marcus Rashford that the Englishman got no contact on. Despite that, the ball trickled past Jordan Pickford in the Everton goal.
With Everton chasing the game late on, Edinson Cavani scored his first Manchester United goal, after Fernandes broke forward from midfield and played him in.
This is the first time that Carlo Ancelotti has lost three successive league games in charge of a club, since November 2006, when he was AC Milan manager.
Here's how each player fared for both teams.
Everton Player Ratings
Jordan Pickford - 5/10
Pickford cannot be held at fault for any of the Manchester United goals, and also made an excellent stop to deny Marcus Rashford. However, he was a little lucky to not concede a penalty for a loose kick on Harry Maguire.
Seamus Coleman - 5/10
Coleman had problems throughout the first half, as Manchester United kept creating overloads against him. James Rodriguez didn't really track back enough, leaving Coleman alone against two attackers. While going forward, Coleman often took on more than he could manage, in trying to dribble past a host of defenders, instead of playing a simple pass or cross.
Michael Keane - 5/10
Both the Manchester United goals in the first half came as a result of Everton allowing an attacker to creep in between their two centre-backs. As the more senior centre-back, Keane should have taken more responsibility for organising the defence.
Mason Holgate - 4/10
Holgate's return to the Everton starting lineup was not a happy one. He was caught ball-watching instead of stopping Fernandes from heading the ball for the first goal. His distribution was also surprisingly below-par.
Lucas Digne - 6/10
Digne's crossing was a disappointment today. He linked up well with Bernard for most of the game, and got into excellent crossing positions, but overhit most of them.
Allan - 5/10
Allan had an intriguing battle with Fernandes throughout the game, but came out second best. The Portuguese drifted all across the pitch, and made it difficult for Allan to keep a tabs on his movement.
Gylfi Sigurdsson - 4/10
It has to be mentioned that Sigurdsson's set-pieces all game were atrocious, as they hardly got past the first man. He was the first Everton player to be substituted, with Iwobi replacing him.
Abdoulaye Doucoure - 6/10
Doucoure played reasonably well for most of the game, and could have altered the result right at the death. He had two big chances, but put one shot high and failed to make contact on another.
James Rodriguez - 5/10
James showed isolated moments of his class with his passing, but for most of the game, he was a passenger. He made life difficult for Coleman by not tracking back.
Bernard - 7/10
Bernard was Everton's best player on the day. He gave Aaron Wan-Bissaka a difficult afternoon with his dribbling and movement in from the flank. He opened the scoring as well, with a placed shot that left David de Gea flapping.
Dominic Calvert-Lewin - 6/10
The Englishman's aerial presence was not used well enough by Everton throughout the game. His flicked header set up Bernard's goal, but after that, there was little to no service into thei big striker.
Alex Iwobi - 6/10
Iwobi looked bright after coming on to replace Sigurdsson in the second half. He helped Everton maintain the width on the right flank, but like the rest of his team-mates, his crossing was not good enough.
Cenk Tosun - 4/10
Nothing that Tosun did on the pitch was of any impact to an Everton side who were chasing them. Some of his passes were misplaced by considerable margins as well.