This was a Romelu Lukaku-Marcus Rashford show that José Mourinho and Manchester United will hope can run and run. The Belgian’s double put United in pole position – before late strikes from Anthony Martial and Paul Pogba – and Rashford again proved he can be the X-factor the manager desperately requires if he is to lead United to a 21st championship. By the hour here Mourinho’s side were stroking the ball around and through West Ham in an impressive fashion witnessed only sporadically last season.

Rashford played a key part in one sequence that closed with an offside Henrikh Mkhitaryan finish, while Lukaku ran across the line and into deep positions to pose the Hammers awkward questions.

Eighty-four days after United’s previous Premier League game their mission of converting last season’s 15 draws into victories began with Lukaku as the spearhead. The 24-year-old is the No9 Mourinho bought, for £75m, to provide a similar weight of goals to Zlatan Ibrahimovic, who managed 28 in all competitions last season.

Seventeen of those were in the league, seven fewer than Lukaku’s haul for Everton. The new man’s key role in the Mourinho masterplan was illustrated early. Lukaku is a powerful man and when he biffed aside a defender, then later rose to a high ball in the penalty area it was clear that if United are to prosper Lukaku has to fire, too.

Those unwanted 15 draws caused United to limp to sixth place, only securing a Champions League berth by winning the Europa League. Ten were here, at a venue that demands entertainment as the minimum offering. If, say, just half those draws had been wins at Old Trafford then United’s final points tally would have risen to 79, enough to finish third.

United managed only 54 goals last season, an obvious factor in the lack of wins. Quizzed about this in the buildup, Mourinho acknowledged the need for more goals from those around the No9. The XI he sent out could be billed as forward thinking. Ander Herrera was a surprise omission as the Portuguese sacrificed a midfielder for an extra forward. This was Juan Mata who lined up alongside Mkhitaryan, the No10, and Rashford, the left-sided wide man.

The trio were stationed behind Lukaku in a 4-2-3-1 but if all want to be chosen consistently they will have to register more than the 15 goals they returned between them in the last league campaign. Inside a stadium louder than it has been in recent times, United hogged the ball and moved it menacingly on occasion during the opening half. This allowed Mata to move behind for a chance that was blocked, but when in a second time he did not hit the ball instantly. At this juncture United could be accused of a lack of directness in the last third. This has been a complaint about the post-Sir Alex Ferguson teams and when they did finally register it was via some quick thinking.

Rashford relayed the ball to Lukaku and he followed Tuesday’s Uefa Super Cup consolation in the 2-1 loss to Real Madrid by crashing a shot in off Joe Hart’s right-hand post to make it 1-0.

Rashford’s pace gives United’s frontline a crucial dimension and he continued to light up the side when they roved forward. Mourinho’s recognition of this may have prompted him to allow the 19-year-old to flit across positions. After the opener Rashford switched from left to right to create problems along that wing. Then, he hung around next to Lukaku to make it a dedicated two-man strikeforce. By the close of the first half he was back on the left and could wander off surely to hear a contented half-time word from his manager.

The question now was could United go on and convince they could be prolific goalscorers this season. In just seven of their 19 league outings here last season they scored two or more. This again points to the fault of the attackers, plus Jesse Lingard, Martial (on the bench on Sunday) and even Pogba, whose return of five was underwhelming for a footballer of his talent. In that 2-1 loss to Real, Mourinho referred to a late chance Rashford spurned that would have taken the game into extra time.

Almost as soon as Martin Atkinson blew for the second half Rashford missed a near-identical opportunity. The teenager raced clear but missed badly to the left of Hart.

United were soon in total control, though, as Lukaku made no mistake with his head and that was a second league goal for the home crowd to enjoy as Mourinho’s team finished the game far more dangerously than they started it. Rashford hit a post before Martial and Pogba made it 4-0 to send supporters home buzzing.

When Rashford was replaced by Martial on 79 minutes Lukaku wandered over to him to pat his cheek. There already seems a telling understanding between them.

It is, of course, very early days for the Lukaku-Rashford pairing and for this United side, whose next test is at Swansea on Saturday. Yet the early signs are there that this could be a year to remember for United. As Mourinho said: “After many years of Premier League experience, I keep my feet on the ground. But fans have reasons to be optimistic because we are.”