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Philippe Coutinho has scored in his past two Merseyside derbies

Liverpool enhanced their prospects of a top-four place by beating derby rivals Everton, whose own hopes of breaking into the battle for a Champions League qualification spot were severely damaged by the defeat.

Sadio Mane gave the hosts an early lead when he played a one-two with Roberto Firmino and finished off an angled run with a shot into the far corner.

A Philippe Coutinho shot was palmed up by Toffees keeper Joel Robles and headed off the line by Phil Jagielka before the visitors equalised.

Jagielka flicked on a corner at the near post and, after Ashley Williams got a touch, Matthew Pennington arrived to slot in his first Everton goal on his first appearance of the season.

However, the match was level for just two minutes and 57 seconds before Coutinho beat two players and curled a shot into the top corner, and he then set up substitute Divock Origi - on for the injured Mane - to power in Liverpool's third.

The result leaves the Reds six points clear of fifth-placed Manchester United - who have two games in hand - while Everton are seven points off the top four having played more matches than their rivals.

Coutinho sparkles but Mane injury a worry

Liverpool hired a private jet to bring Coutinho and fellow Brazil international Firmino back after their country's win over Paraguay in midweek and will feel the move was worth it after the forward returned to form in style.

Coutinho has struggled since recovering from an ankle injury in January but provided an assist as well as his goal as the Reds extended their unbeaten run against their Merseyside neighbours to 14 games in all competitions.

The 24-year-old was a picture of feints, shimmies and attacking runs at the Blues defence, and might have scored earlier if Robles and Jagielka had not combined to deny him.

Mane, who scored the winner in the reverse fixture, set the Reds on their way with his 13th goal of the season - but an injury in the second half will be a concern for Liverpool boss Jurgen Klopp, who is already without attacking midfielder Adam Lallana for up to a month.

Senegal winger Mane, Liverpool's top scorer this season, hurt himself trying to win the ball off Leighton Baines and, when he tried to put weight on his leg after treatment, collapsed.

"I've met Mane in the dressing room. It doesn't look too good," said Klopp.

There was a pre-match tribute to former Liverpool captain, coach and caretaker manager Ronnie Moran, who died in March at the age of 83, with a minute's applause and a Bugsy mosaic, in reference to his nickname, on the Kop

Where was Romelu Lukaku?

Everton striker Romelu Lukaku has been accused of going missing in the big games, despite being the Premier League's top scorer with 21 goals this season.

The Belgium international may have scored against top-four sides Manchester City and Tottenham during the present campaign, but he gave his critics further fuel after an ineffective display at Anfield.

He did not have his only touch in the Liverpool area until the 70th minute and he also failed to have a shot - on or off target - on the opposition goal.

"On today's showing, what you saw was a striker who didn't do enough to keep himself on the pitch," BBC Sport pundit Jason Roberts told Final Score.

"In these games where you need him to do a little bit more of the dogged work, he didn't offer that to his team. His head went down and that was the story of Everton."

Midfielder Ross Barkley is also a key player for the Goodison Park club. However, he was also disappointing as he tested referee Anthony Taylor's patience with challenges on James Milner and Emre Can, before being booked for a late tackle on Dejan Lovren.

Romelu Lukaku's touchmap shows he only had one touch in the Liverpool area

Reds hold upper hand on Merseyside

Everton have not won at Anfield since September 1999 and they did little to alter the view that they have a psychological barrier at the home of their neighbours.

Even having gone into the match with one defeat in 12 league games and four clean sheets in their past five games, they could not stop their hosts doing the double over them this season.

However, there were mitigating circumstances with injuries to defenders Seamus Coleman and Ramiro Funes Mori forcing manager Ronald Koeman to replace them with right wing-back Mason Holgate, 20, and centre-back Pennington, 22.

Pennington did have the joy of scoring but was also caught out for Coutinho's goal as Liverpool widened the gap between the two teams to nine points.

Man of the match - Philippe Coutinho

Coutinho has six Premier League assists this season - his best tally so far was seven in the 2013-14 campaign

What they said:

Liverpool manager Klopp on Barkley's challenge on Lovren: "I'm still a kind of a guest in this country. How can I decide what is OK and what is not OK?

"My opinion is that the players should leave the pitch healthy and fit but not injured.

"It's not my job to judge it. If you saw something, say it. If not, be quiet."

Liverpool 3-1 Everton: Liverpool manager Klopp hails 'really good' win

Everton boss Koeman: "Maybe one or two tackles were a little too much. It's football, a derby.

"From both sides I saw tackles that were maybe more than a yellow. According to the bench of Liverpool - I don't mean the manager - the referee should have shown eight red cards."

Everton manager Ronald Koeman unhappy with Liverpool bench red card appeals

Klopp record - the stats you need to know

Klopp is the first Liverpool manager to win his first three league Merseyside derbies against Everton.

Mane has scored in both Merseyside derbies this season, the first player to do that since Luis Suarez and Daniel Sturridge in 2013-14.

Mane has now been involved in 18 league goals this season (13 goals, five assists), his best return in a Premier League campaign.

Pennington became the fifth player - following Duncan Ferguson, John Arne Riise, Raul Meireles and Steven Naismith - to score his first Premier League goal in a Merseyside derby.

Only Olivier Giroud (seven) has scored more goals as a substitute than Divock Origi's six since the Belgium international's Premier League debut in September 2015.

What next?

There is a fast turnaround in the top flight with a midweek programme in which Everton visit Manchester United on Tuesday for a 20:00 BST kick-off and Liverpool host Bournemouth on Wednesday, also at 20:00.