And, as befits a player who will be being paid somewhere in the region of £500,000 (€570,000) for the next four-and-a-half years at Old Trafford, it was a debut, in modest surroundings, which spoke volumes about his hunger to get his United career up and running.
After a cautious opening, it was Sanchez who set up United’s opening goal four minutes before half-time, playing a short pass that offered Marcus Rashford the chance to launch himself on one of his mesmeric runs into opposition territory.
Defender Tom James actually took the ball off the England forward at one stage, as three defenders converged on Rashford, only to stand off and allow his opponent the chance to regain possession and force the ball into the Yeovil goal from six yards.
But, while Ander Herrera, Jesse Lingard, and Romelu Lukaku eventually ensured his team a comfortable passage into the fifth round, Yeovil had made by far the stronger start as United, and their newest asset, settled into unfamiliar surroundings at Huish Park.
“These matches are difficult if the attitude is not correct,” Mourinho said. “In the first half they gave us a difficult time, pressing and aggressive on the ball and on the shinpads. I could hear Darren Way on the touchline, he knew what he was saying, they were organised.
“But in the second half we had control of the game and had more space and more quality, we killed the game.
“Alexis Sanchez is a fantastic addition, everyone is happy that he comes. Good players want good players. The question is always which one is going to be left out, it is not about that for us.
“We have a fantastic group of attacking players and he is another one with more maturity and experience. His choice for the second goal is a choice that a player like Marcus Rashford is too nervous to make that kind of decision. He brings maturity and class.” The early signs with Sanchez could be described as rusty, in particular a couple of badly hit long passes.
But, slowly and surely, Sanchez and United found some sort of groove and by the midpoint of the first half, the increasingly effective Sanchez set up Scott McTominay for a shot which Artur Krysiak in the Yeovil goal did well to turn away at full stretch.
Sanchez was beginning to look more like the player who sparked this month’s unholy transfer scramble, one which ended up seeing the exchange of swathes of money which could have wiped out the debt of a small third-world nation.
His touch, strength, and purpose grew more threatening with every passing minute — and Yeovil knew it, in particular centre-half Nathan Smith who earned a booking on the half hour for a foul on Sanchez that presented the new boy with a 25-yard free-kick which beat the wall but not Krysiak who dived sharply to smother.
It was a poor challenge by Smith, one which might have merited a straight red on another day, although Yeovil’s efforts hardly would have deserved having another obstacle placed in their way.
In fact, they continued to trade blows with United effectively. Before the interval, Carrick’s foul on Lewis Wing resulted in a free-kick on the edge of the United area which full-back James punched through the crowded area and which Romero, in turn, punched away.
Predictably, though, Sanchez was not finished and his assist ensured United took a precious lead into the interval, although it was coming at some cost for the debutant as, within seconds of the restart, Sowunmi became the latest home player booked for a foul on him.
Within five minutes, Rashford should have doubled the lead, from another Sanchez assist, but saw his shot deflected over for a corner from which Mata’s cross-shot landed on the roof of the goal.
Sanchez remained alert but, with the lead so slender, Yeovil still offered Mourinho concern which made it all the more cruel that the second goal came on a devastating counter from a 61st minute Yeovil corner.
United quickly turned defence into a four-on-three attack which ended with Mata and Sanchez feeding Herrera who finished clinically from a dozen yards.
Mata had a tap-in correctly ruled out for offside and any hope lingering in Yeovil hearts must have evaporated a few moments later when the United man was replaced, by Lukaku.
Soon after that, Mourinho had seen enough, calling an end to Sanchez’s debut after 72 minutes and allowing him an ovation from visiting supporters.
Thereafter, Sam Surridge and James, for Yeovil, were denied by solid goalkeeping but Lingard ensured a truly emphatic victory two minutes from time when he drove a low shot into the far corner after an exhilarating right-wing run and Lukaku volleyed in a fourth in injury-time from close range after more excellent play and a cross from Lingard.
Krysiak 7; James 6, Sowunmi 6, Smith 6, Dickson 6; Green 7 (Fisher 69, 6), Wing 6, Bird 6 (Browne 55, 6), Gray 7; Zoko 6, Surridge 7 (Smith 80, 6).
Romero 7; Darmian 6, Lindelof 6, Rojo 7, Shaw 6; Herrera 7, Carrick 7, McTominay 7; Mata 6 (Lukaku 64, 7), Rashford 7 (Gomes 87), Sanchez 8 (Lingard 72, 7).
P Tierney 7.