Manchester United enter Thursday’s 174th derby with Manchester City knowing victory at the Etihad Stadium will leapfrog them over Pep Guardiola’s side into fourth place after this convincing win.

Yet José Mourinho suggested winning the Europa League, another route into the Champions League, is preferable. “If we beat Celta we go to the final and, yes, it is important to us to play in the Champions League but this club wants trophies. We have 25 per cent chance to win the Europa League.”

Before the recalled Wayne Rooney’s 251st goal for the club Anthony Martial became the first United man to score at Turf Moor in the league since Lou Macari in 1976. In doing so he cost another £8.5m payment to Monaco, a clause being triggered by Martial reaching 25 goals for the club. This may raise his fee to £44.5m but the near £40m dividend yielded if Champions League qualification is achieved means United will hardly care.

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Mourinho had implored Martial to up his performance level and afterwards he said: “Yes, it was very good. With the ball, without the ball, in the middle of two strong central midfielders, without anyone behind him because we had no No10.”

In characteristic manner the Portuguese again entreated Chris Smalling and Phil Jones to hurry up recovery from injury and be available for City. “Eric Bailly was incredible. If I was Smalling or Jones, I would play Thursday. I wouldn’t accept one guy to play nine matches in a row because I am injured,” said Mourinho. “If they have a crazy mentality like I have [they can play]. If they are safe thinking and are surrounded by people with the mentality they have, it is more time.”

On 90 minutes Paul Pogba was replaced by Michael Carrick and he was later seen hobbling to the team coach. “I don’t know if he is injured or just super-accumulation of fatigue in the muscles,” said Mourinho. “If he cannot play Thursday, he cannot play and we play another one. We don’t cry, like today. We cry because we have two important injuries, two important surgeries and periods of recovering and we feel for our friends.”

This referred to the serious knee injuries suffered by Zlatan Ibrahimovic and Marcos Rojo. While United’s players donned T-shirts featuring one of their names during the warm-up, Mourinho said: “I just think about them and like everybody I’m really sad.”

Mourinho had talked of protecting his players following Thursday’s 120 minutes against Anderlecht and made eight changes. Only Pogba, Bailly and Jesse Lingard were retained, with Rooney the notable inclusion. This was only a second league start since 17 December for the captain, who had clocked up only 86 minutes in total since 1 February.

Sean Dyche’s XI showed only Andre Gray in for the injured Sam Vokes in the manager’s belt-and-braces 4-4-2. United lined up as a 4-3-3 that put Martial as the central striker with Rooney and Lingard left and right of him.

The first half’s finest move resulted in the opener. This was a one-two fashioned over 70 yards as Martial collected, ran forward and passed right to Ander Herrera. The midfielder returned the ball to the Frenchman, who continued his run and nosed it coolly beyond Tom Heaton for a fourth league finish.

This was 21 minutes in. As the match passed the half-hour Robbie Brady spun in a dangerous ball from the right and later the same player swung in a free-kick from the left which caused Daley Blind to watch Ben Mee carefully while shepherding the ball out.

As the break neared, disaster struck at the other end for Burnley. Pogba held off Joey Barton and found Martial. His effort was half-blocked and Rooney doubled the lead. Gray went close with a shot but at the break United’s cutting edge gave them a deserved lead.

The question then was whether Burnley could grab a goal and affect United’s rhythm. Their problem continued to be final-third execution, with Brady often a culprit with aimless passing during the second half’s opening exchanges.

Later Pogba showed the winger better use of the ball with a 25-yard shot at Heaton, which had the keeper sprawling left to prevent a third for the visitors. From here United coasted home after Michael Keane missed a late chance.

Burnley have collected an admirable 32 points at this venue, the division’s sixth best home haul. They have beaten Liverpool and drawn with Chelsea and this was only their fifth defeat before their own crowd.

But Dyche’s squad are enduring a concerning wobble with only one win in 11 outings. They are only five points above the drop zone before travelling to Crystal Palace – who are two points above – on Saturday. “There is still work to be done,” the manager said.

Another indicator of what Mourinho is building is that his team are now 23 league games unbeaten, the best sequence in six seasons. “It compensates the fact we are not good at home,” said the manager.

Now comes the trip to east Manchester for a crucial showdown with Guardiola’s men.