Antonio Valencia, Anthony Martial and Romelu Lukaku scored as United responded to leaders Manchester City’s first Premier League loss with a third win of the calendar year to cut the gap to Pep Guardiola’s men to 12 points.
Jose Mourinho’s attention will now turn to transfers, with City understood to have stood aside in the pursuit of United target Alexis Sanchez, while Lambert will focus on elevating Stoke out of the bottom three when he starts work today.
What may happen in the transfer window was inescapable at Old Trafford, particularly when the teamsheet came out and there was no Henrikh Mkhitaryan in the United squad.
The Armenian has been mooted as a potential makeweight with Arsenal in any Sanchez deal and in a pre-match interview with Sky Sports Mourinho admitted Mkhitaryan’s absence was down to “doubts about his future”.
His omission meant Juan Mata and Martial occupied the flanks and the former’s pass into the Frenchman led to seventh-minute penalty shouts, ignored by referee Anthony Taylor, when Stoke debutant Moritz Bauer fell into Martial with his arms draped on him.
United did not have to wait long for their opener as their first shot resulted in a goal. Valencia, back after a month out injured, collected a Pogba pass on the edge of the box, moved to his left and, showing no sign of his previous aversion to his weaker left foot, rifled beyond Jack Butland.
Stoke developed a habit of folding when going behind in the latter days of Mark Hughes’ reign but they responded well. Stephen Ireland, playing in the Premier League for the first time since May 2016, was particularly bright and nutmegged Pogba at one point.
However, he showed all the rustiness of a player who had been out for so long when firing two opportunities wide, the second after he had been left all alone from 15 yards out.
Stoke were still knocking on the door and, when Peter Crouch beat David De Gea to Bauer’s deep cross, Eric Maxim Choupo-Moting latched on to the loose ball with a shot that Phil Jones blocked.
Such profligacy was always likely to haunt the visitors and so it proved when Martial added a second seven minutes before the break.
Again it was Pogba who provided the assist with a smart pass across the box that Martial whipped into the net with a measured first-time strike.
De Gea denied Xherdan Shaqiri just before half-time and there was no sign of Stoke fighting back upon the resumption, despite extended chants of “Paul Lambert’s Barmy Army” by their supporters.
Pogba would have chalked up a third assist had Butland not stopped Martial almost walking the ball in and Mata nearly picked out the bottom corner.
A third always looked likely and United wrapped up the points 18 minutes from time. Stoke appealed in vain for handball when Martial’s pass was controlled by Lukaku, the Belgian holding off Kevin Wimmer and turning a low shot home for the 50th goal Stoke have conceded in the league.
A 51st almost arrived when Pogba’s cross was flicked on to the post by Mata and Lambert, watching from the directors’ box, did not even see a consolation goal as De Gea thwarted substitute Mame Diouf.