It took United a while to break down a stubborn Yeovil defence but they finally did four minutes before half-time when Marcus Rashford took advantage of a mistake to open the scoring for Jose Mourinho's men.
Ander Herrera then made it 2-0 just after the hour mark before late goals from Jesse Lingard and Romelu Lukaku sealed an easy win in the end for United, who now await the draw on Monday evening to see who they will get in the next round.
Sanchez made his United debut as Mourinho made ten changes to his starting eleven
As was expected before the game, Mourinho made plenty of changes to his starting eleven with Alexis Sanchez making his debut for the club, while Michael Carrick made his first start for United since September 20th due to injury.
The hosts started brightly and had a great chance to take the lead
The game itself saw the Glovers start really brightly and they had a great chance to take the lead early on when Jordan Green managed to get through the United defence unchallenged, but his weak effort from a difficult angle was easily saved by Sergio Romero.
United, though, then started to finally take control of the game when Sanchez started to get on the ball more and he almost created the opening goal half an hour in.
Sanchez's influence on the game grew as Rashford took advantage of a mistake to give United the lead before half-time
Sanchez played a brilliant pass to Scott McTominay on the edge of the box but the midfielder's shot was well-saved by Artur Krysiak, who did well to keep the ball out of the net.
United kept pressing right until the end of the half for an opening goal and finally it did come four minutes before the break when a mistake from Tom James allowed Rashford in on goal to calmly curl the ball into the back of the net.
Therefore, at the break, United led in the game that they found very difficult early on as the hosts really put themselves about in a game that they wanted to give everything in to try and cause an upset.
A slow start to the second half ended when United doubled their lead
After half-time, the game took a while to get going but when it did, United doubled their advantage with their first real attack of the second half.
The goal came after a blistering counter-attack from United ended with Sanchez playing a great ball through to Herrera, who slammed the ball home with his left foot.
The second goal really did knock the stuffing out the hosts and the visitors nearly made it 3-0 when Lingard, on as a second-half substitute, played a great ball through to Rashford but the striker was denied his second goal of the game by a good save from Krysiak, who done well to get off his line so quickly.
Gomes made an appearance from the bench as goals from Lingard and Lukaku sealed easy progress for United
As the game was heading into injury time, United added two more goals to put gloss on the win as Angel Gomes came on as a substitute before the end and looked really bright.
The third goal was scored by Lingard, who scored a fantastic solo goal after receiving the ball from a Matteo Darmian throw-in, while Lukaku added a fourth with the last kick of the game after a brilliant cross from Marcos Rojo.