Another poor day for Bournemouth brought the Cherries closer to returning to the Championship as they remain stuck in the bottom three after taking a shock lead by Junior Stanislas at Old Trafford.
Greenwood, Rashford from the penalty spot, and Martial's teenage phenomenon hit back half-time.
The victory puts Ole Gunnar Solskjaer's men in fourth position a point above Chelsea as they continued an undefeated streak that stretched back to 16 games in January.
United had kept 11 clean sheets without loss in their previous 15 matches, but defensive lapses have been the only blight for Solskjaer on another rewarding afternoon.
Both were guilty as Stanislas nutmegged the world's most expensive defender and then fired in on De Gea 's near post entirely against the 16 minute run of play.
This time, the mistakes were not as costly as Greenwood, Martial and Rashford's blossoming front three quickly turned the game around.
Greenwood's star is rising rapidly and the 18-year-old blasted Fernandes' pass home to get United back on track.
Martial completed the package with a spectacular shot from outside the box to go for the first time in his career to cross 20 goals in a season.
The game appeared to be over at the break but Bournemouth was presented with a path back into the game by a poor start from United.
At half-time, Eric Bailly substituted Victor Lindelof and the Ivorian managed a loose pass from Nemanja Matic as he sought charge.
Josh King, who was a United target in January when Solskjaer looked desperately for cover for the then-injured Rashford, dispatched the penalty and seconds later Bournemouth had the ball in the net again only for Arnaut Danjuma to be flagged offside.
Rashford also had another goal ruled out for offside, but United were happy to settle for five as they moved into the top four for the first time since September.
Bournemouth remain second bottom and without a point in four games since the Premier League's restart.