The Swans, bottom of the table before kick-off and without a victory in 15 previous league visits, became the first team since Manchester United a year ago to inflict a home defeat on the Reds.
They did it the hard way as well as after Llorente had put them into a surprise 2-0 lead just after half-time. A double from Roberto Firmino levelled things up, with the visitors indebted once again to Gylfi Sigurdsson for their winner.
Tweet of the match
"All the good work in recent weeks for LFC gone with that spirited display from SwansOfficial. Very poor at the back especially Klavan" - Mick Quinn (mickquinn1089) suggests Liverpool's defence should shoulder some responsibility for the result.
Fernando Llorente. The Spaniard's goals may be the difference between survival and relegation and while his first was something of a gift his second, a powerful header, was a classic striker's effort.
Liverpool have conceded more goals (27) in the Premier League this season than any other side currently in the top seven.
In with the crowd
Anchorman in midfield? Hollywood A-lister Will Ferrell made an appearance in the directors' box wrapped up against the cold.
Who’s up next?
Liverpool v Southampton (EFL Cup, Wednesday January 25)
Swansea v Southampton (Premier League, Tuesday January 31)
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