Fernando Llorente and Roberto Firmino both bagged braces before the Swans' Icelandic forward wrapped up the points in an enthralling second half.
Swansea City clambered off the foot of the Premier League table with a thrilling 3-2 victory over title hopefuls Liverpool at Anfield.
A first half of few opportunities offered little indication as to what was to follow, with Fernando Llorente netting twice inside seven minutes of the re-start – poking home from a corner before powerfully turning in a header.
The hosts hit back through a brace from Roberto Firmino, with the Brazilian’s second seeing him control the ball expertly on his chest before crashing a half-volley into the back of the net.
It was, however, to be the Swans that had the final say, with Gylfi Sigurdsson slotting past Simon Mignolet in the 74th minute to snatch all three points.