It was his second goal in as many league games after also scoring in the 3-0 win over Brighton at the end of last month.
Junior Stanislas scored the opener for Bournemouth as he nutmegged Harry Maguire before beating the equally hapless David de Gea at the near post from a tight angle.
Mason Greenwood has now scored eight league goals for United in 2019-20; among players aged 18 and younger, only Michael Owen (twice), Robbie Fowler and Wayne Rooney have scored more in a Premier League season.
Bournemouth pulled a goal back in the 50th minute when Josh King converted his penalty, but Greenwood soon restored Manchester United's two-goal cushion with a superb strike in the 54th minute.
"He's here to do one thing, and that is play football and become as good as he can be. If he keeps his head on his shoulders, which I think he will, he'll be a player for many seasons to come".
Major West Bank annexation move not imminent: Israeli minister
The Oslo agreements of the 1990s envisioned the status of the West Bank being resolved in negotiations. He proclaimed that the illegal Israeli West Bank settlements were not illegal.
United's invigorated front three of Mason Greenwood, Marcus Rashford and Anthony Martial grabbed the headlines by each contributing goals to the rout as they helped extend their team's unbeaten streak to 16 games across all competitions.
It generally goes without saying that any successful side needs to turn their home ground into a fortress.
Leicester City, three points ahead of us at present, host Crystal Palace in a match which kicks off also at 3pm.
Next up, Man United hit the road to take on Aston Villa on Thursday away from home.
Once with his left and once with his right at an empty Old Trafford, Manchester United's 18-year-old forward made the ball look and sound like it had been fired from a cannon, living up to the song that describes him as dynamite. Fernandes has scored seven goals and provided five assists in 14 appearances since joining from Sporting Lisbon in January.