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Gylfi Sigurdsson scored the winner to seal Swansea's first league victory at Anfield

Swansea lifted themselves off the bottom of the Premier League table and dealt a huge blow to Liverpool's title hopes with a thrilling win at Anfield.

Gylfi Sigurdsson scored from close range with 16 minutes left to give Paul Clement his first win as Swans boss and the club their first away league victory over the Reds.

Roberto Firmino had struck twice to draw the hosts level after Fernando Llorente's two goals in four minutes after the break.

The defeat leaves Liverpool seven points behind leaders Chelsea, who now have a game in hand, at home against Hull on Sunday.

The Tigers are one of three teams, along with Sunderland and Crystal Palace, leapfrogged by Swansea, who move up to 17th after only their second win in eight league games.

Swansea looking up

Swansea had previously failed to win any of their 15 league visits to Liverpool

In the wake of last weekend's demoralising 4-0 defeat by Arsenal, Clement said Swansea would be "naive" to ignore the possibility of Premier League relegation this season.

On the evidence of their performance at Anfield, it would be equally naive of anyone to write them off.

In the space of seven days they have gone from a side who collapsed at the first setback to one capable of rallying under extreme pressure.

Their first-half defensive display - which saw them restrict Liverpool to a couple of half-chances - belied their status as the club with the division's most porous defence.

Their second-half performance was clinical, epitomised by Llorente's two strikes - a close-range finish following Federico Fernandez's header from a corner, followed by a header from Tom Carroll's cross - and Sigurdsson's decisive, well-placed finish. These were their only three efforts on target.

It was also gutsy. They had to dig very deep against a side who, before Saturday, were unbeaten in the league in over a year at home and who had scored 26 goals in their previous nine league games.

Liverpool stumble again

The average positions for each side give an indication of the balance of play, with only Llorente (9) in the opposition half for Swansea

In the programme for this match, Liverpool boss Jurgen Klopp described October's encounter with Swansea in Wales - a 2-1 win sealed by a late James Milner penalty - as "one of the toughest we have had all season."

The German may feel the need to revise that after Saturday's game.

Despite having Philippe Coutinho back in the side - and ending the game with Divock Origi and Daniel Sturridge on the pitch - the Reds were short of attacking invention and strength in the absence of Sadio Mane, who is at the Africa Cup of Nations with Senegal.

Their failure to move the ball quickly enough in the first half meant they did not properly test Swansea's packed defence.

And while Firmino scored his first goals in six games - the first a header from Milner's cross, the second a fierce finish after he had chested down Georginio Wijnaldum's delivery - a total of five shots on target and an Adam Lallana deflected effort against the bar is scant product from nearly 75% possession.

With this result coming after successive away draws at Sunderland and Manchester United, the Reds are in danger of allowing a title challenge to slip away before February has even begun.

Their next game, at home to the league leaders, is now surely a must win.

Man of the match - Fernando Llorente (Swansea)

He may not be as mobile as he once was, but Llorente still knows where the goal is. This was his third Premier League double of the season.

What the managers said...

Liverpool manager Jurgen Klopp: "It's hard to accept. In the first half we created four or five chances which we didn't take.

"The start of the second half we were poor and then we played brilliantly and scored two. Then we were a bit passive and one player was alone in our box, which is completely senseless.

"The most disappointing moment was the third goal and I can't explain it as we had so many chances to challenge.

"It's really difficult to accept at this moment. It is fair Swansea won, no - but was it deserved, yes."

Liverpool 2-3 Swansea: Jurgen Klopp criticises Reds' defensive 'switch-off'

Swansea manager Paul Clement: "We frustrated Liverpool and defended really well. We showed great togetherness and it was a massive team effort.

"At half-time I told the players we would get at least one chance, but to get three was unbelievable.

"It's very important for the confidence of the side that we can come to a big team and get a result. We need to work hard on the training pitch and make sure we get another result in 10 days' time."

Clement 'very proud' of Swans effort

Reds first to 50 goals - the stats you need to know

Liverpool's unbeaten Premier League run at Anfield has ended after 17 matches (11 wins, six draws).

Firmino has scored three goals in his past two Premier League games against Swansea.

Llorente has now scored eight Premier League goals but his first two away from home.

Liverpool conceded three goals at Anfield in a league game for only the second time under Klopp.

The Reds are the first Premier League team score 50 goals this season, while Swansea are the first to concede 50 (both now on 51).

Swansea have won back-to-back away league games in the same season for the first time since May 2015.

What next?

Liverpool will attempt to overturn a 1-0 deficit when they host Southampton in the EFL Cup semi-final second leg on Wednesday (kick-off 20:00 GMT). The Reds then welcome Wolves to Anfield in the FA Cup fourth round on 28 January (12:30), before another home game - the big one in the Premier League against Chelsea - at 20:00 on 31 January.

Swansea's involvement in the FA Cup ended in the last round so their next game is at home against Southampton in the Premier League on 31 January (19:45).