Before the end of the opening quarter of an hour, Omar Sowunmi should have done better with a header from 12 yards, with Romero barely having to move to make the save.
Sanchez did not really have an influence on the match until the 25th minute when he set up Scott McTominay inside the penalty area, but the youngster's low strike was superbly clawed away by Artur Krysiak low down to his right.
As the first half progressed, Sanchez sent a free kick too close to the goalkeeper before dragging a 16-yard effort wide of the far post, but United were still able to take the lead just before the break.
There appeared to be no danger when Tom James had the ball inside his own penalty area, but the young Welshman failed to clear and Rashford got ahead of the defender before finding the bottom corner from eight yards.
Yeovil needed a fast start to the second half but United were unfortunate not to double their advantage within six minutes of the restart, with Rashford first seeing a shot deflected just wide after taking the ball past two players.
From the resulting corner, Juan Mata attempted to take advantage of a quick short corner but his cross evaded everyone, clipped the crossbar and went over.
The home side had half a chance to equalise when Bournemouth loanee Sam Surridge won a header at the back post, but the youngster's header went well off target.
From that moment, it was one-way traffic in United's favour and it came as no surprise when the visitors doubled their lead, with Sanchez playing his part in the goal.
Mata started a United counter which eventually resulted in Sanchez teeing up Herrera inside the penalty area, with the Spaniard sending a low shot into the bottom corner of the net from 14 yards.
Mourinho took the chance to make a couple of substitutions with Sanchez's debut coming to an end in the 72nd minute, shortly after shaking off an ankle knock.
Angel Gomes was given his second appearance in a United shirt during the closing stages and almost scored within 20 seconds of his introduction but after taking the ball past the defender, the 17-year-old curled the ball into the side-netting.
However, moments later, Lingard added a third with a fine individual goal, racing from the right flank before sending the ball into the far corner of the net from 14 yards.
The scoring was still not complete, with Lukaku getting on the scoresheet with the final attack of the game after being able to convert Marcos Rojo's cross into the top corner from six yards out.
YEOVIL TOWN (4-5-1): Krysiak; James, Sowumni, Smith, Dickson; Gray, Wing (C.Smith 83'), Bird (Browne 56'), Green (Fisher 69'), Surridge; Zoko
MANCHESTER UNITED (4-2-3-1): Romero; Darmian, Lindelof, Rojo, Shaw; Carrick, Herrera; Mata (Lukaku 65'), McTominay, Sanchez (Lingard 72'); Rashford (Gomes 88')