Manchester United have “earned the right” to challenge for a top-four finish in the Premier League after a “fantastic” spell of post-lockdown form, says boss Ole Gunnar Solskjaer.

United maintained their relentless pursuit of a place in the Champions League with a hard-fought win against Crystal Palace at Selhurst Park.

Solskjaer’s side were under pressure after Leicester City’s earlier victory over Sheffield United and responded with a victory that keeps them in fifth place, level on points with the Foxes but with an inferior goal difference.

It extended United’s unbeaten run to 19 games in all competitions, and Solskjaer believes United, who are still in the FA Cup and Europa League, have set themselves up for a thrilling end to the season.

“No-one thought in January that we would be in with a shout for top four,” he said.

“We have done fantastic since the restart. These are the games that matter. That is the thing at Manchester United, you have to step up and show your personality.”

United were made to work for their victory, Marcus Rashford breaking the deadlock with a stylish finish in first-half stoppage time before playing his part in a sweet move involving Bruno Fernandes that was rounded off by Anthony Martial in the 78th minute.

Palace felt a real sense of injustice, furious that they were denied a penalty just before United took the lead when Wilfried Zaha tangled with Victor Lindelof, and then seeing a potential 55th-minute equaliser from Jordan Ayew ruled out by VAR for a very marginal offside.

It meant Roy Hodgson’s side slumped to their sixth consecutive league loss and their night was made worse when defender Patrick van Aanholt suffered a dislocated shoulder after trying to prevent Martial scoring United’s second.

United set up date with destiny

United were not at their best and were grateful to goalkeeper David de Gea for some fine saves, particularly from Zaha, while he also did well to keep out Luka Milivojevic’s free-kick.

This, however, is a United team developing a ruthless streak, demonstrated by Rashford’s calm finish for the opener, and then an artistic move constructed by Rashford and Fernandes that enabled Martial to complete the job in style.

United needed the instant response after Leicester’s win earlier on Thursday and there is real efficiency as well as a rapier thrust to Solskjaer’s side that has taken them on this long unbeaten run.

It leaves them in contention for that top-four place, as well as the Europa League, and they also have an FA Cup semi-final against Chelsea at Wembley this weekend.

Most mouth-watering of all, they face a potentially decisive visit to Leicester on the final day of the season.

Palace cursing their luck

Palace’s season is fizzling out after their latest loss, the promise of that impressive first post-lockdown win at Bournemouth seeming an age away.

This, however, was no tame surrender and Palace gave a good account of themselves, only to be undone by United’s quality.

And certainly Hodgson and his players will feel they were hard done by when their appeals for a penalty as Zaha tangled with Lindelof were ignored.

Palace chairman Steve Parish expressed his frustration on social media. “Is the VAR broken? Serious question,” he tweeted.

There was more frustration when Ayew’s 55th-minute finish at the far post from Zaha’s cross-shot was ruled out after a lengthy VAR inspection, the striker being ruled offside by the thinnest of margins.

“Certainly we are not fortunate at the moment. The gods of fortune are not smiling on us with certain decisions,” Hodgson said afterwards.

“We have won games and got good results against top teams like Manchester United playing a lot worse than we did tonight.”

Palace are comfortable in 14th place but there is no question the end to their season has been something of an anti-climax.

Man of the match – Marcus Rashford (Man Utd)

Unbeaten run continues – the stats

• United have gone unbeaten in their last 19 games in all competitions (W14 D5) – their longest such run since a 29-game streak ending in November 2010 under Alex Ferguson.
• Roy Hodgson has lost six consecutive Premier League games for the first time since losing his last three with Blackburn in November 1998 and his first three with Fulham in January 2008.
• Palace remain winless in their last 16 home Premier League encounters against ‘big six’ sides (D3 L13) since a 2-1 victory against Chelsea in October 2017.
• Seven goals which were originally awarded against United have been overturned by VAR this season, the joint-most of any side in the Premier League this campaign (alongside Southampton and Brighton).
• Anthony Martial and Marcus Rashford have now assisted one another a combined seven times in this season’s Premier League, the most of any pairing in a single season for Man Utd in the competition.
• Timothy Fosu-Mensah made his first league appearance for United since May 2017, three years and 56 days ago; only Paul Pogba (4y 154d in Aug 2016) and Will Keane (4y 44d in Feb 2016) have had a longer gap between appearances for the club in the Premier League.

What’s next?

While Palace are away at Wolves on Monday (20:15 BST), United are getting ready for an FA Cup semi-final with Chelsea at Wembley on Sunday (18:00 BST).

More to follow.