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The former Norwich City and Aston Villa boss was appointed as Mark Hughes' successor earlier in the day and was in the stands at Old Trafford as Eddie Niedzwiecki oversaw his one game as caretaker manager.
Stoke's resistance took just 11 minutes to be broken as Antonio Valencia marked his first game back from injury by cutting in from the right and curling an unstoppable left-footed effort into the far corner, leaving Stoke stopper Jack Butland grasping at thin air.
United doubled up after 38 minutes with an even better strike. Man-of-the-match Paul Pogba squared the ball to Anthony Martial on the edge of the box and the Frenchman whipped a sumptuous first-time effort into the top right-hand corner.
And a routine win for José Mourinho‘s side was wrapped up in the 72nd minute when got his reward for an excellent night's work. The big Belgian controlled Jesse Lingard's fizzed ball into his midriff before stepping away from Bruno Martins Indi and Kevin Wimmer to lash home.
But what did we learn from a routine win at Old Trafford? Here are the biggest talking points from Monday night's offering.
Mkhitaryan set for Arsenal switch?
For all the talk of Alexis Sánchez being a Manchester United transfer target building up the game, it was the future of one of United's own which dominated the headlines once the teams were announced as there was no place for Henrikh Mkhitaryan in the matchday 18.
The Armenian has been underwhelming this season and made just four Premier League starts since the end of September. His future has been subject of intense speculation with reports the 28-year-old will be a makeweight in a deal to bring Sánchez to Old Trafford.
But he was left out of United's squad altogether for the visit of Stoke which only served to pour fuel on the fire. And, speaking beforehand, Mourinho claimed the winger was not fully committed to the club.
“I would lie if I said it was a pure tactical decision,” he said. “It was just a choice of the players that we know, in this moment, they have 100 per cent their heads in Manchester United.
“No doubts about the future. I don't think it's easy for a player to play when there are doubts about his future. It's added pressure that a player doesn't need, so I think it's the best for him and for us, while the doubt is in the air, to protect him.”
Shaw shows there is a way back under Mou
At the end of last season Luke Shaw‘s long-term future at Old Trafford looked bleak as long as Mourinho remained at the helm. The Portuguese was scathing in his criticism of the England international, even going as far as to say he had to think for the left-back in a 1-1 draw with Everton in April.
“He [Shaw] had a good performance but it was his body with my brain,” said Mourinho. “He was in front of me and I was making every decision for him.
“The communication was possible because we were very close. I was thinking for him, when to close inside, when to open, when to press the opponent, I was making every decision for him.”
But Shaw was bullish in his riposte, stating his desire to knuckle down, re-double his efforts and prove his manager wrong.
“It is my time to fight until the end of the season and show the boss what I can do and what I can bring to help his team,” Shaw said soon after. “I remember having the meeting with him and I said to him at the end, ‘I am going to prove you wrong’ because I believe and I want to do that, not just for myself but the fans that have been behind me and sent me really nice messages and want to support me through this time.”
It was a laudable stance to take but, knowing how stubborn Mourinho can be, his appeared a lost cause.
Two Carabao Cup appearances and 137 minutes of action were all the 22-year-old had to show for the first three months of the season. Mourinho could not even find a spot on the bench in the Premier League for the former Southampton prodigy who looked destined for the exit door.
Yet, out of blue, Shaw was thrown a lifeline for the visit of Bournemouth on December 13. It was his first Premier League start since the 1-1 draw with Swansea City on April 30. He has started six games since, missing only two, and was included against Stoke tonight. Perhaps, then, his future is not as clear-cut as it might have appeared?
Mourinho's famous assertion it Mo Salah for evidence. By giving Shaw a second chance, Mourinho might have saved his own blushes and the defender's United career.
United full-backs unpick Potters
It took just 11 minutes for Mourinho's side to open the scoring and it was little surprise to anyone inside Old Trafford that the goal came from one of the full-backs.
Even before the returning Valencia had cut inside Josh Tymon and crashed a ferocious left-footed strike into the top corner, the Ecuadorian was causing the young defender problems.
It was the same on the opposite flank where Shaw, miraculously back in the side of late, was giving Potters new-boy Moritz Bauer a Premier League crash course in the form of the runaround.
With nominal wingers Juan Mata and Martial driving inside Manchester United left plenty of space in the channels for Valencia and Shaw to attack and the duo did so with relish, as you can see from the heatmap below, courtesy of WhoScored.com.
Stoke need upgrade a left-back
This isn't going to be an assassination of Tymon. The Stoke No.12 was caught out on both of United's first two goals and was generally given a torrid time by the fit-again Valencia. But it is hardly his fault.
At just 18 he was signed as one for the future. Prior to moving to the Bet365 Stadium he had just 12 senior career appearances to his name, all at former club Hull City and only five of which had come in the Premier League.
He is still very much in the developmental phase of his career and a prospect. Not a first-team regular. In fact, Hull vice-chairman Ehab Allam has even gone as far as claiming the England Under-20 international made the wrong decision in joining Stoke.
In October, he told the Hull Daily Mail: “I don’t think Josh has done himself any favours. I believe it was the wrong move to go to a club where he’s not playing regularly.
“Here he could have been a first choice at left-back, playing every week. If he’d been playing well, then he would have got an improved contract again.”
But injury to regular left-back Erik Pieters saw seen him thrust into the starting XI for the visit to Old Trafford; just his second league start of the season – and it showed.
He was dragged out of position and left Stoke exposed down the left flank on several occasions. In fairness, he was not helped by Eric Maxim Choupo-Moting playing ahead of him; the Cameroonian failing to track back to help the teenager out when required.
Mercifully the youngster was withdrawn at the interval in favour of the more experienced Wimmer who fared little better. New boss Lambert will already know that tightening up a porous backline is imperative the Potters' survival hopes. Finding cover at left-back to avoid having to pitch Tymon in again before he is ready will be a similarly high priority.
Work to do for new boss Lambert
Watching on from the stands at Old Trafford, Lambert will be itching to get to work tomorrow morning having replaced Hughes following the Potters' humiliating FA Cup defeat to Coventry City.
The 48-year-old would have been reasonably encouraged by the way his side caused their illustrious hosts a few problems defensively – particularly in the first half when David de Gea had to be at his best to deny Xherdan Shaqiri.
But the Potters were soundly beaten by a United side who did not have to get out of first gear very often in order to secure a comfortable victory.
It will have been little surprise to Lambert that his new side have the Premier League's worst defensive record. At times United toyed with the Potters' backline and for Lukaku's goal, in particular, the visitors were so passive the Belgian was able to breeze clear of Martins Indi and Wimmer before firing home his side's fourth.
The Potters' midfield was bypassed almost completely and they never got to grips with United's press. Mourinho's men hunted in packs to win the ball back and Stoke were powerless to resist. But it shouldn't be a surprise to see a midfield including Stephen Ireland bested by man of the match Paul Pogba and Nemanja Matić.
Lambert has a big job on his hands.