Junior Stanislas fired the visitors into a 16th-minute lead but United hit back through Greenwood before Rashford converted a penalty and Martial rifled a screamer into the top corner to give the home side a 3-1 halftime lead.
Martial completed the set with a stunning strike from outside the box to reach 20 goals in a season for the first time in his career.
However, arguably more important than his talent is his mentality and fans have spotted how something he did after scoring showed he has the right temperament to go the distance with United.
Greenwood continued his incredible first season in the top flight by scoring his 14th and 15th goals of the campaign as United defeated the Cherries 5-2.
The latter's 15-goal haul is obviously his best, as this is the first time he's played more than four games in a season.
One of the most striking things about the Red Devils during this time has been their ferocious attack.
"I thought we were a genuine goal threat in the match".
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"I think we've seen improvement from Mason, Martial and Rashford and they will keep on improving, but we will never standstill. He knows where to finish if it is on the training ground, here or in his garden at home".
Providing the teenager can join Rashford and Martial by passing the 20-goal barrier it will be the first time that three United players have done so in the same season since 1964-65, when Denis Law (39), David Herd (28) and John Connelly (20) did likewise.
Solskjaer also mentioned Greenwood in the same breath as Rooney, when speaking about the 18-year-old following the game.
Victory takes Ole Gunnar Solskjaer's men a point above Chelsea into fourth as they extended an unbeaten run stretching back to January to 16 games.
That restored United's two-goal lead at 4-2 after Josh King's penalty for Bournemouth, and Fernandes added a fifth off a free kick from the edge of the area in the 59th.
"If he shoots he will score, he is going to get better and his general play has improved".