By the end Wayne Rooney could probably be forgiven for wondering what kind of adventures he might be missing with his old team. He had heard his name sung and, before he disappeared into the tunnel, there was a little, polite wave of appreciation. Yet Rooney wore the look of a man whose return to Old Trafford had felt like an ordeal and he can never have imagined there would come a time when he would find himself in the away dressing room ruminating on what it is like to be in the relegation zone.

The paradox is that this was not always the fluent, dangerous Manchester United that has been seen in other parts in the new season and it felt slightly perplexing that José Mourinho described it as their best performance so far. Indeed, for a long part of the second half they had flirted with the idea of letting their opponents back into the match and there was clear evidence of how much they would miss the injured Paul Pogba.

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Ultimately, though, it turned into the third 4-0 win of their opening five league fixtures and another reminder of the team’s firepower. It is the first time United have won their opening three home games since the 2011-12 season and they are level with Manchester City at the top of the Premier League on identical records: 13 points, 15 goals scored, two conceded. Pep Guardiola’s team are top solely because their second name starts with a C rather than a U.

Everton, in stark contrast, find themselves in the bottom three on the back of that late flurry of goals when Henrikh Mkhitaryan (83 minutes), Romelu Lukaku (89) and the substitute Anthony Martial (92) quadrupled the score and Rooney, chin in hands, watched forlornly from the dugout, having just been substituted.

Antonio Valencia had opened the scoring, four minutes in, with a firecracker of a shot and these feel like difficult moments for Ronald Koeman and his players. Everton have now gone six games in all competitions without a victory, losing the last four with a combined score of 0-12, and have not won in the league since the opening weekend of the season. “Please be realistic,” Koeman said afterwards, taking issue with Mourinho’s reference to Everton being a club that had ambitions of a top-four finish. The reality, however, is that Everton’s supporters were entitled to expect more after an extensive period of summer recruitment.

A lot of those fans had already left by the time Martial’s penalty, after a Morgan Schneiderlin handball, completed the scoring. They enjoyed that moment in the first half when Lukaku shot wide when it seemed certain he would score. Yet they also had to endure being shushed by their former striker after he had set up Mkhitaryan’s goal. Lukaku had been booed by the away end and, when he added the third goal, he made a beeline towards the Evertonians, cupping his ear as if to ask why the volume had suddenly gone down.

As for Rooney, he found it difficult early on to provide any evidence that he can still flourish at United’s level. He did, however, grow into the game and became a difficult opponent for Eric Bailly in particular. It needed David de Gea’s quick reactions to deny Rooney an equaliser early in the second half and it was something of a surprise that Koeman removed him in the 81st minute. At the risk of sounding slightly cruel it was a better performance than the crowd here became used to seeing from Rooney in recent seasons. Throughout the middle hour of the game there was not actually a great deal between the two teams. Yet Valencia’s goal was a beauty and it is difficult to think of any other time in his eight years at Old Trafford when he has struck a shot more powerfully. United’s captain was 20 yards from goal, aiming diagonally from close to the far corner of the penalty area, when Nemanja Matic’s crossfield pass curled his way and he let fly.

The noise of the crowd made it clear they had witnessed something special and the ball flashed past Jordan Pickford at the kind of speed that makes it harsh, perhaps, to question the goalkeeper. Even so, an argument could be made that the shot was central enough to be saved. Hypothetical, perhaps, but it is difficult to think De Gea would have been beaten that way.

Even in a four-goal win De Gea showed again why he is so valuable with second-half saves from Rooney and Gylfi Sigurdsson. An equaliser would not have been implausible at that stage but it was still more likely that the home team would score next.

Mkhitaryan swept a low shot past Pickford to soothe the crowd’s nerves and Lukaku’s seventh goal in seven games for his new club came from close range in a crowded penalty area. Lukaku’s free-kick had bounced back off the defensive wall but Matic fired the loose ball back in and United’s £75m striker had dashed forward, anticipating the ball might come back his way. How Everton miss him.