Just 15 minutes into the game, the visitors were already 1-0 up. United have had all of the ball, but one cross into the area caused issues for their defence.
Stanislas picked up the scraps and, after easily getting past Maguire with a nutmeg, he slots in beyond De Gea at the near post.
Greenwood levelled the score with a powerful effort before the half-hour after Bruno Fernandes sets him up for the equaliser.
He unleashed a brilliant strike that Ramsdale could only parry up into the net.
Rashford then converts from the spot-kick to complete the turnaround for United after a handball from Smith, who clearly handled from Martial’s header.
VAR checks confirmed the decision and Rashford sent a low finish into the bottom-right corner. Ramsdale guessed the right way, but couldn’t get down to it.
Before Martial curled in an excellent third all in first half. Fernandes fed it out wide, with Shaw making a good overlapping run to give Martial the space to cut inside and, from there, the France international plants a wonderful finish into the top-right corner.
A bad pass then put Matic in trouble, and United’s midfielder had to hammer it back to his defence. His pass was a poor one, with Bailly attempting to jump up and control it on his chest. It strikes the top of his arm, just on the edge of the area, and Mike Dean points to the spot.
There was course for VAR check and penalty was awarded. King stepped up and hammers it home from 12 yards to make the scoreline 3-2.
Only for Greenwood to double his tally of the game and also for United with an incredible goal. The Red Devils were under pressure but they managed to keep a move alive after a bit of pinball in the area.
The ball falls to Greenwood and, after skipping away from Ramsdale, the youngster slams a fantastic right-footed finish into the top-right corner.
United’s star man – Bruno Fernandes also gets into the scoresheet as he curls a strike into the left-hand corner to make it 5-2 for the host
An ultimately comfortable victory for United and Ole Gunnar Solskjaer will be proud of his boys.
Bournemouth, meanwhile, are entrenched in the relegation zone, with time running out to escape it.