If only Manchester United could play Fulham every week people might begin to take them more seriously. The joke before kick-off at Old Trafford was that Liverpool had done United a favour by winning so handsomely at Bournemouth, because goal difference might be important in the battle for eighth place.

Enter the Premier League’s bottom club, with a performance to prove the table does not lie, and suddenly United are not just above Bournemouth but up to sixth. Admittedly Everton do not play until Monday but José Mourinho will take what he can at the moment.

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“We are unbeaten in four league games,” the allegedly happy one said beforehand, which was one way of putting positive spin on the fact United had not picked up a win since before Bonfire Night. “We were good at every level in the first half,” the manager said. “We played like I want us to play, we were a compact unit that gave Fulham no chances.”

Fulham were kind enough to let United boost their goal difference with their biggest win of the season, and although a significant gap remains to the top five, Mourinho and his players are at least in the right place to be pushing for a Champions League spot.

On the edge of the European positions sounds a lot better than mid-table obscurity, though a truer test will come at Anfield next Sunday. Claudio Ranieri’s strugglers were far too easily dominated, with the Italian reduced from an early stage to standing on the touchline with a resigned look and extended right hand to show his players the direction they were supposed to be playing. With just Aleksandar Mitrovic ploughing a lonely furrow up front it never happened, and Fulham looked beaten from the moment Ashley Young opened the scoring.

The United captain initially appeared likely to attempt a cross when he took the ball high on the left but once he beat Denis Odoi to find space in the area he caught sight of goal and found Sergio Rico’s top corner with a curling right-foot drive.

Juan Mata scored next, applying a confident finish after Marcus Rashford cut back the ball from the goalline. Romelu Lukaku was criticised earlier in the week for not doing much except trying to score goals, so he should be quite proud of the pass that played Rashford behind the Fulham defence. Rashford then had the awareness to pick out Mata at the back of the penalty area, and when his shot beat Rico’s dive the contest was as good as over.

The Fulham fans certainly seemed to think so. “You’re nothing special, we lose every week,” was the chant from the travelling support.

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Rico produced a good stop to keep out a thunderous free-kick from Rashford, before United increased their lead just before the interval with a slick triangular passing move that clearly pleased Mourinho. Jesse Lingard found Mata, whose first-time ball along the six-yard line was neatly tucked away by Lukaku.

Fulham showed a little more life after Ranieri made two half-time substitutions, though their best chance in open play fell to André Schürrle following a weak clearance by Diogo Dalot, and the winger skied his shot. It summed up Fulham’s afternoon when less than two minutes after Aboubakar Kamara had pulled a goal back from the penalty spot, following a foul on the substitute by Ander Herrera, they went down to 10 men when a studs-up challenge on Rashford by André-Frank Zambo Anguissa brought a second yellow.

Any hopes of United running up a cricket score were dashed when Rico managed saves from Rashford and then Lukaku, although the goalkeeper was beaten at his near post when Rashford scored an audacious fourth from the angle of the area.

Had Fred not tried a risky pass rather than a straightforward one in stoppage time United might have hit five in the league for the first time since Sir Alex Ferguson stepped down.

In the end Fulham were not quite that obliging but it was close. “It is quite simple,” Ranieri said with his usual pithiness. “If we play like we did in the first half, we will be relegated. Play like we did in the second and we can survive.”