Manchester United took advantage of Manchester City’s defeat at Liverpool to close the deficit to 12 points with this accomplished win. It is still a chasm but José Mourinho and co will feel better and the club will be boosted further should they secure Alexis Sánchez, with them now firmly in pole position to do so. Paul Lambert, the newly appointed Stoke City manager, watched on from the posh seats but saw United again deny the Potters victory here, their last coming in April 1976.

Of the display Mourinho said: “I didn’t like the first half. I only like [our] two amazing goals. We were confident and organised but a bit slow. The second half was totally different. We accelerated the game.”

The Portuguese made six changes from the FA Cup win here a week ago. Once again Henrikh Mkhitaryan was excluded completely – due to “doubts about his future”, Mourinho said – while Romelu Lukaku started for the first time in more than a fortnight following a head injury.

Eddie Niedzwiecki’s XI showed seven players different from the Cup defeat at Coventry City , with Stephen Ireland’s first league start in 996 days notable, alongside the debut of Moritz Bauer, a 25-year-old Austrian.

City’s defeat by Liverpool on Sunday should have been ample inspiration for United to make a bright start. Anthony Martial was the first to do so, roving down the left before hitting in a cross Stoke managed to clear. Bauer’s first act in English top-flight football was to appear to fell Martial in the area as the Frenchman chased a Juan Mata ball. From the turf Martial made the appeal but Anthony Taylor, the referee, was unmoved.

So, too, was Jack Butland, when United opened the scoring on nine minutes. This was because the visiting goalkeeper was given zero chance from Antonio Valencia’s vicious swerving left-foot shot that rocketed past him.

The captain’s third of the season came courtesy of Paul Pogba’s searing run-then-pass that drove United from near halfway to near goal, before Valencia did the rest.

This was the kind of dazzling play United are capable of and which makes the yawning gap to City a puzzle. Mourinho had spoken of the benefit of the warm-weather break in Dubai last week and there was an obvious freshness about United. Yet he will have been unhappy at the space Luke Shaw allowed Bauer to run into when Joe Allen slid the ball down the left-back’s corridor. Suddenly Stoke were in behind but Bauer failed to find a team-mate.

Pogba was in imperious form, though. One stepover swept him infield and, when his pass found Jesse Lingard, the No 10 drew a foul. Up stepped Mata from 25 yards but his free-kick crashed into the wall.

Ireland’s radar had already gone awry when he found himself in front of David de Gea and pulled the trigger. Again he missed the target.

Anthony Martial scores Manchester United’s second goal in the 38th minute. Photograph: Simon Stacpoole/Offside/Getty Images

This showed that Stoke could get at what was an uncharacteristically open Mourinho team. When Bauer mishit a cross it became an awkward high ball at which De Gea flapped. The ball bounced to Eric Choupo-Moting but the finish lacked composure.

This came during a passage of play in which United struggled to escape from their half. When they finally managed this, Lukaku pinged in a cross towards Lingard and a corner was claimed.

It came to nothing as did a Mata fall in the area that Bruno Martins Indi believed was a dive, though the No 8 was keen to deny this. At the break, though, Stoke were two behind: Martial’s sweet finish from outside the area coming after Pogba rolled the ball expertly to him.

For the second half Niedzwiecki took off Joshua Tymon for Kevin Wimmer. United began with a move that took in Martial, Lingard, Pogba, Lukaku and Mata, the ball struck around with unerring accuracy.

To enjoy total control United required a third, given the amount of time remaining. Martial burst through on Butland but the keeper smothered well. Next Pogba – yet again – probed, finding Lukaku. The centre-forward turned and fired a shot that had power but went too easily into Butland’s hands.

At this point the travelling support began singing “Paul Lambert’s barmy army”, which will have cheered the watching Scot. He could also be content with the quality his new side had displayed. The confidence shown was hardly that of a side lying third from bottom.

Martial was putting in a fine performance but really should have finished from close range yet, once more, he steered the ball straight at Butland. United’s issue of failing, at times, to kill opposition off was again evident when Lingard fed Mata and the forward’s attempted curler missed to Butland’s left.

When United put the ball in the net for a third time, on 66 minutes, Mata was adjudged offside. There was no doubt about Lukaku’s later finish, though, the Belgian scoring, under pressure, to close the match out.

Of Stoke’s survival hopes, Niedzwiecki said: “It’s a big challenge staying in the Premier League. We’re still in the pack and now’s the time for everyone to get behind the new manager.”