It was some calling card Anthony Martial left behind on his first appearance at Old Trafford and some way to introduce himself to a crowd who, if they are anything like Wayne Rooney, will probably admit they did not know a great deal about the athletic, high-kneed attacker Manchester United have turned into the most expensive teenager on the planet.

The money is astronomical enough that even Louis van Gaal has described it as “ridiculous” but there are not too many better ways to repay some of the transfer fee than scoring the goal that sealed victory against the club United want to beat more than any other team.

There were four minutes of normal time to go when Martial collected the ball on the left and, for the first time, United were suddenly looking vulnerable. They were leading 2-1 but Christian Benteke had scored with a scissor-kick that was executed with such stunning quality as to lift the entire Liverpool team.

Instead, the ball reached Martial in the kind of position where a teenage Cristiano Ronaldo danced and showboated his way into Old Trafford’s affections on an equally memorable debut against Bolton Wanderers 12 years ago. Martial saw a gap between Martin Skrtel and Nathaniel Clyne, cut inside and trusted himself to get there. It needed tenacity as well as skill and the teenager’s perseverance took him where he wanted to be. His shot was dispatched with the calmness of a player who seemed at complete ease with his new surroundings and in that moment Old Trafford was given a better idea why the club had recruited the 19-year-old for an initial £36m, with another £22m in potential add-ons.

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It was a wonderful way to mark his debut, coming on as a 65th-minute substitute on a day when David de Gea’s return to the team added to the sense that at least United are gradually heading in the right direction. This was Van Gaal’s 51st match in charge and his tally of 28 wins is only one better than David Moyes’s total over the same period. The team do not always thrill in the way of old and the first half was another reminder that Van Gaal’s “process” – the buzzword that seems to have taken over from “philosophy” in his football lexicon – can jar with what many Old Trafford match-goers traditionally expect. All the same, there was a clear imbalance of talent throughout the game and United did find a penetrative edge in the second half. Liverpool, in contrast, were slightly directionless for long spells and took an age before examining whether De Gea might be slightly rusty after his time out.

The irony was that Van Gaal, with his love of rhythmic control, commented afterwards that he had preferred the first-half performance, regardless of the lack of excitement. Others would surely contest that a side featuring the creative sparks of Juan Mata, Memphis Depay and Ander Herrera should be capable of getting behind the opposition defence with greater frequency. Instead, they often fell into the trap of aiming crosses towards Marouane Fellaini and hoping to capitalise on the aerial ability of the player who was deputising for the injured Rooney. It was a bland 45 minutes and Liverpool’s only serious problem came when Simon Mignolet’s throw struck Mata and left Fellaini with a chance he wasted.

The breakthrough came four minutes into the second half when Mata played a clever free-kick to Daley Blind and the Dutchman scored with a controlled, rising shot. Liverpool’s defence had been waiting for a cross that never came. Mata squared the ball to Blind, who was loitering behind the main pack of players, and the deception worked perfectly.

Liverpool can reflect on a couple of chances to equalise, with some excellent defending from Blind to thwart Skrtel and Danny Ings in quick succession. De Gea briefly created some problems for himself with a poor throw and kick but United looked a more rounded team with him back in goal and the one-handed save to keep out Ings’s bouncing effort was a reminder of his qualities.

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Later, there was another splendid save to turn away the substitute Jordon Ibe’s rising shot but it would be misleading to dwell too much on these chances because the truth for Liverpool, as Brendan Rodgers acknowledged afterwards, was that they did not use the ball well and left Benteke too isolated.

Herrera doubled the lead from the penalty spot after Joe Gomez misjudged his sliding tackle on the Spaniard and United were relatively comfortable until Benteke sent a brilliant, twisting volley past De Gea. Briefly, there was the possibility of a comeback, but Rodgers did not try to spin the narrative afterwards. Liverpool’s manager conceded it had been a dishevelled performance and, apart from Benteke, the game’s outstanding performers all wore United’s colours, most notably Blind and Luke Shaw. Bastian Schweinsteiger had his best game since moving to Manchester and, as the crowd headed away, there was the clear sense that Martial’s tour de force will linger long in the memory.