On evenings such as these Erik ten Hag must feel he has the golden touch. It was not without a by now customary spot of bother but Manchester United racked up a fourth successive win for the first time this season, the substitute Scott McTominay’s powerful late header helping them to cut the gap to the top four to six points.

Presumably the main question on the lips of fans and the thing whirring around Ten Hag’s head is: why did it take so long to get into this groove?

McTominay gave Rasmus Højlund, who opened the scoring, a ­piggyback as United’s players celebrated before the away fans. Højlund exhi­bited his predatory instincts to score his sixth goal in his past seven ­appearances. But Douglas Luiz cancelled out that strike midway through the second half, at which point Aston Villa undoubtedly had United on the ropes.

Related: Aston Villa 1-2 Manchester United: Premier League – live reaction

It was not quite the late, late show United required at Wolves 10 days before, McTominay scoring with 86 minutes on the clock, but it no doubt tasted just as sweet for Ten Hag.

Was this the night when United lasered in on their rivals? It certainly felt a significant result, United finally winning away at another team vying for a Champions League berth. It seemed they sensed the importance of victory, too. Villa, who dropped to fifth after Tottenham’s late win against Brighton, appear stuck in the mud, the wheels of Unai Emery’s machine are spinning but with little to show for it. Since losing at United on Boxing Day, they have taken seven points from the past available 18, their two wins coming against teams ensconced in the relegation zone in Burnley and, more recently, Sheffield United.

In the absence of Lisandro Martínez it was over to Harry Maguire to play left-sided centre-back alongside ­Raphaël Varane, who was ­promoted to the starting lineup. Maguire and Varane are both predominantly right‑footed but Ten Hag selected the former to play next to Luke Shaw given the rapport they have built on England and United duty. Shaw was replaced by Victor Lindelöf at the break, a precaution given his injury record, and Villa preyed on Lindelöf’s vulnerability at left-back.

Gareth Southgate was among those in the stands who will surely have been encouraged by Maguire’s assured display. He made a smart block to deny Jacob Ramsey a clean shot at goal as Villa cranked up the ­pressure in search of an equaliser midway through the first half, making a long barrier with his right leg, and had a key hand in Højlund’s goal on 17 minutes. Maguire eluded his marker, Boubacar Kamara, and got above Diego Carlos to nod down Bruno Fernandes’s corner and an unmarked Højlund stroked in from a couple of yards out.

Maguire and United had to do their fair share of defending. A couple of minutes into the second half André Onana repelled Ollie Watkins’s first‑time shot from Matty Cash’s cross, the Villa striker nipping in front of Varane, and in the first half Onana had to make a two-handed save to deny John McGinn after the Villa captain leathered a vicious strike at goal with his laces. Leon Bailey bent a shot wide after cutting in from the right and Ramsey missed after being slipped inside by Àlex Moreno down the left. Emery winced as the chances piled up.

United had the advantage but no such control. Fernandes earned a high-five from Maguire after ­making a block on the edge of ­United’s 18-yard box. Villa found it too easy to bypass United’s midfield and swarmed upfield. It was no surprise when Onana’s net eventually rippled, Douglas Luiz sweeping in Bailey’s cross. Varane hoicked clear a corner but Villa recycled the ball and ­Douglas Luiz side-footed in before celebrating wildly in front of the United defender.

“We can’t lay back, we have to improve our game,” Ten Hag said. “When we were winning the game, we gave them the initiative. We kept them alive and got punished for it.”

It was McTominay, again, who provided the relief. The ­Scotland midfielder has scored crucial winners this season against Brentford, Chelsea and now Villa. Mainoo jinked clear of Ramsey and laid the ball on for Diogo Dalot, who shone at right‑back. Dalot sent in a delicious first‑time cross and McTominay made a ­beeline for the six-yard box, where he beat Cash to the punch and headed in past ­Emiliano Martínez. Cash pulled his socks over his knees as McTominay surged towards the ecstatic away support, who made sure to their let feelings be known.

The first question in Emery’s post‑match press conference served up a chance for the Villa manager to rattle through the positives. He picked out the number of chances his side created – they had twice as many shots on goal as United – and labelled this his side’s most complete performance of the season, but for their win here against Manchester City.

Then, almost 90 seconds later, came the telling line. “But the result was not good and we have to accept it,” Emery said.