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This was a game that will live long in the memory of both sets of supporters.
A sure pick for any classic Barclays Premier League DVD, the Swans were unfortunately edged out by the odd strike in a seven-goal thriller.
But they certainly played their part as Garry Monk's side showed character, desire and flair at Anfield in a breathtaking display.
The hosts had raced ahead after just three minutes through Daniel Sturridge after the England international rounded Michel Vorm and fired home.
And when Jordan Henderson doubled the lead after 20 minutes, it looked like a painful afternoon lay ahead for the visitors.
But two goals within four minutes had Monk's side on level terms.
First, in front of the Kop, Jonjo Shelvey curled a sublime effort past Simon Mignolet via the crossbar - a strike which had the whole of Anfield up on its feet applauding - and then Wilfried Bony's header deflected off Martin Skrtel soon after.
But the Reds were ahead at the break as Sturridge nodded home Luis Suarez's cross in a frenetic first-half.
There was never any danger of the pace dropping, and just 70 seconds into the second half the Swans were awarded a penalty as Bony went down under Skrtel's challenge.
The Ivorian stepped up and fired into the bottom corner for his 19th goal of the season to send the back on level terms.
Both sides pushed hard for the winner, and Liverpool eventually got it as Henderson tapped home after Vorm had done miraculously well to deny Suarez.
Defeat left the Swans on 28 points from 27 games, but they will have taken plenty from this performance ahead of Thursday's Europa League decider in Napoli.
The Swans made three changes to the starting XI.
Following the Europa League draw with Napoli, Ben Davies hadn't made this trip due to a slight calf problem so fellow Wales international Neil Taylor started at left-back, while former Liverpool midfielder Jonjo Shelvey and Jonathan de Guzman went into midfield at the expense of Jose Canas and Pablo Hernandez.
Shelvey, who scored against his old club in the 2-2 draw earlier in the season, made his first start since the defeat at West Ham on February while, on the bench, another former Red David Ngog was among the visitors' substitutes.
Brendan Rodgers opted for three changes to his starting XI from the FA Cup defeat to Arsenal.
Simon Mignolet returned in goal as Brad Jones dropped to the bench while Glen Johnson went in at right-back in place of Aly Cissokho. Daniel Agger was the final change as he started in central defence with Kolo Toure dropping to the bench.
LIVERPOOL:Simon Mignolet, Glen Johnson, John Flanagan, Martin Skrtel, Daniel Agger (Kolo Toure, 63), Steven Gerrard (capt), Jordan Henderson, Raheem Sterling (Joe Allen, 58), Philippe Coutinho (Victor Moses, 79), Luis Suarez, Daniel Sturridge.
SUBS: Brad Jones, Joao Teixeira, Iago Aspas, Aly Cissokho.
SWANS: Michel Vorm, Angel Rangel, Chico Flores, Ashley Williams (capt), Neil Taylor, Leon Britton, Jonathan de Guzman (Pablo Hernandez, 73), Jonjo Shelvey (Jose Canas, ht), Nathan Dyer (David Ngog, 78), Wayne Routledge, Wilfried Bony.
SUBS: Gerhard Tremmel, Jordi Amat, Dwight Tiendalli, Marvin Emnes.
The Swans got off to a disastrous start as they fell behind after just three minutes.
After Raheem Sterling pinched possession off Angel Rangel in the Liverpool half, the winger raced on before sliding a perfect through ball for Daniel Sturridge, who rounded the onrushing Michel Vorm before firing into an empty net.
Brendan Rodgers' side almost doubled their lead shortly after as Sterling cut inside from the left before firing towards goal, but Vorm dived at full stretch to tip it wide.
The Swans needed to respond, and Wilfried Bony volleyed over from 20 yards before the striker was just beaten to a low Neil Taylor cross following a Jonathan de Guzman through ball.
It looked more promising for the Swans, and Jonjo Shelvey drove on before seeing his 25-yard strike deflected for a corner before another attempt from the midfielder drifted high and wide.
But just as the Swans were enjoying a brighter period, the hosts doubled their lead on 20 minutes.
Sturridge cut inside from the right and teed up Jordan Henderson on the edge of the box, and he fired into the top corner from 20 yards.
But the Swans hit back immediately, with it proving third time lucky for Shelvey after 23 minutes.
And there was no luck involved in the strike itself, with Dyer finding his team-mate 20 yards out, and Shelvey's first-time curling effort bounced in via the crossbar.
It was a fantastic strike, and even the home crowd burst into a round of applause for the quality of the strike from the Liverpool man.
And the comeback was complete four minutes later as Bony's header from a de Guzman free-kick deflected off Martin Skrtel's shoulder and past Simon Mignolet.
It was thrilling stuff, with the promise of more goals.
And another did follow, unfortunately for the Swans it came for the hosts after 36 minutes.
Luis Suarez's perfectly judged cross found Sturridge, and the striker leapt to nod home into the corner past a helpless Vorm.
Suarez then attempted to lob Vorm from 45 yards, but the Uruguayan's chip dropped wide.
The Swans replied through Bony, whose low drive was padded wide for a corner by the stretched Mignolet.
And from the resulting delivery, de Guzman found Angel Rangel, but the Spaniard couldn't direct his header on target.
And, in the final act of the half, a swift breakaway saw de Guzman find Dyer on the right, and when Rangel's run distrated Skrtel, the winger had time to line up a shot but it drifted wide.
It proved an thralling first half, with the Swans taking confidence from their comeback although they went into the break trailing.
HALF-TIME: Liverpool 3 Swans 2
Garry Monk made a change at the break as Jose Canas replaced Shelvey.
And within 70 seconds the visitors had a glorious chance to level as they were awarded a penalty as Bony went down under the challenge of Skrtel as Dyer's cross curled into the box.
Bony picked himself up and dusted himself down to take the spotkick, and he found the bottom corner.
It was just what the Swans needed, but Liverpool were quickly on the search to regain their lead.
And Suarez was again menacing as he got onto a through ball in the box, but Vorm came to the rescue to palm it wide.
The pace of the game was frenetic, and after Dyer was fouled 25 yards out by Skrtel, de Guzman's free-kick dropped inches wide of giving the Swans the lead.
Brendan Rodgers made a change before the hour mark as former Swan Joe Allen came on in place of Sterling.
Just moments after his introduction, the Swans carved open a big opportunity as Bony latched onto a misplaced pass and his backheel sent de Guzman in on goal, but his shot was kept out by the foot of Mignolet.
It was end-to-end stuff, and Liverpool probed again as Henderson found Sturridge in space, but the striker's chip dropped wide.
Then Allen pinched possession off Chico Flores ten yards inside the Swans half, and the midfielder found Sturridge, but a superb covering tackle from Ashley Williams deflected it for a corner.
Monk made a further change as Pablo Hernandez replaced de Guzman with 17 minutes remaining.
But the Spaniard had barely been on the pitch 60 seconds when the hosts regained the lead.
After Vorm had spectacularly saved Suarez's initial shot, the loose dropped to Henderson, who tapped home from two yards out.
Monk responded by making his last change as former Reds striker David Ngog replaced Dyer as the Swans went in search of yet another equaliser.
But Liverpool were continuing to look for another as Steven Gerrard struck the post, and then saw Vorm deny him as the time ticked towards the end of the 90.
That was the end of the action though as the Swans left point-less but with their heads held high.