Fernandes curled in a sensational shot from 25 yards out to put United three ahead in the 29th minute of Sunday's (AEST) friendly at Old Trafford.
A large crowd was treated to a superb first-half display from United, albeit Rafael Benitez evidently has work to do heading into his first season as Toffees boss.
Jordan Pickford, making his first appearance of pre-season after helping England to the UEFA Euro 2020 final, was partly at fault for United's eighth-minute opener, Lucas Digne's header catching the Everton goalkeeper cold, with Mason Greenwood on hand to pick up the scraps.
Pickford was beaten again seven minutes later, another returning England international Harry Maguire powering home a brilliant header home from Luke Shaw's corner.
With Fernandes having compounded Everton's misery, Solskjaer was able to make plenty of changes in the second half as he prepares for a tough start to the Premier League campaign against Leeds United.
It was one of those substitutions – Diogo Dalot – who capped things off with the final action of the game, his header looping in over Asmir Begovic.
Andros Townsend hit the crossbar and Demarai Gray missed a golden chance as Everton toiled before Dalot's header.
There was no United debut for Jadon Sancho, while Raphael Varane's move from Real Madrid is still being finalised.
The Toffees face Southampton in ex-Liverpool manager Benitez's first competitive game in charge.