LONDON - Matteo Darmian inspired Manchester United to victory over Crystal Palace and Liverpool crushed derby rivals Everton 4-0 as both teams enhanced their chances of securing European football on Wednesday.

Italian right-back Darmian scored his first goal for United and created an own goal for Damien Delaney as fifth-place United beat Palace 2-0 to close to within a point of fourth-place Arsenal in the Premier League. Divock Origi scored but was then stretchered off as Liverpool outclassed Everton to remain within two points of sixth-place West Ham United, for whom Mark Noble scored two penalties in a 3-1 defeat of Watford. "I was very happy with the performance, but we should have scored many more goals," said Manchester United manager Louis van Gaal.

The teams finishing fifth and sixth stand to qualify for next season's Europa League, with the top four spots yielding passage to the Champions League. Van Gaal's side continue to have designs on the elite competition after warming up for Saturday's FA Cup semi-final against Everton by overcoming fellow semi-finalists Palace at Old Trafford.

Darmian helped the hosts get off to an ideal start as his cross was turned in by Palace centre-back Delaney for a fourth-minute own goal. With Wayne Rooney once again operating in central midfield, United created a string of opportunities and added a second in the 55th minute when Darmian slammed home from the edge of the box. "It was a surprise for us, especially with his left foot!" said United centre-back Chris Smalling. "What a way to get your first goal."

United trail Arsenal by a point and third-place Manchester City by two, although the north London club have a game in hand at home to West Bromwich Albion on Thursday.

Everton will go into their Wembley date with United on the back of a Merseyside derby hiding at Anfield that means Roberto Martinez's men have now gone seven league games without victory. After a one-sided first half, Liverpool struck twice in four minutes shortly before half-time as James Milner crossed for first Origi and then centre-back Mamadou Sakho to head home.

It was Belgian striker Origi's fifth goal in five appearances, but he was stretchered off five minutes into the second half with a suspected ankle sprain following an ugly foul by Everton centre-back Ramiro Funes Mori, who was sent off. Daniel Sturridge came on for Origi and found the net eight minutes later, tucking away Lucas Leiva's pass, before Philippe Coutinho bent in a low shot from the edge of the box to complete the scoring in the 76th minute.

"I would like to say yes, I am delighted, but the injury to Divock Origi has cost me some joy," said Liverpool manager Jurgen Klopp. "I can't say too much about Origi, but they say it is disgusting, awful pictures. But it's not broken, it is a twisted ankle. He is on crutches walking around, so we will have to see."

Everton manager Martinez said: "It was a disaster. A horrible showing that started with the best intentions, but ended up with the inability to get the basics right. "The top and bottom is that we didn't cope with the emotions of the occasion. (There is) a feeling of embarrassment."

Liverpool climb to seventh place, two points below West Ham, whose fine season continued with victory over Watford. Andy Carroll put West Ham ahead in the 11th minute before home captain Noble scored from the spot either side of half-time. Sebastian Prodl replied for Watford with an assured 64th-minute finish, but substitute Troy Deeney saw a stoppage-time penalty saved by West Ham goalkeeper Adrian and Nordin Amrabat was then sent off for a second yellow card. "We are victims of our success as the bar is always more and more up," said West Ham manager Slaven Bilic. "We are coping with that well."