Firmino got in on the act again with 25 minutes remaining, rolling the ball into an open net from Salah's lay-off. After the game, you look and it's 5-0 and you think: 'Wow, 5-0.
Coutinho needed just six minutes to conjure some typical magic when he curled the ball in from distance.
It was his 19th Premier League goal from outside the penalty area and only Steven Gerrard (33) has now scored more from distance for Liverpool. Wayne Routledge crossed for Ayew but his header had no power and was saved down low by Simon Mignolet.
After some good work inside the box, Alex Oxlade-Chamberlain scored Liverpool's fifth of the night with the outside of his boot. The Swans have registered just three wins so-far this season. Keeping things secure at the other end consistently while the goals continue to fly in will surely see Klopp's team to a top-four finish.
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After Paul Clement's sacking last week, managerless Swansea enter the game rock bottom of the table, with only three wins all season. The goals came because we let them cross, which is what happens in a football game.
But in added time Roque Mesa nearly threw it away by giving away possession to Salah and although his pass put Firmino clean through with only the keeper to beat he dragged his shot wide. In the first half he was right full back, he was left full back, he was everywhere. Paul Clement subsequently lost his job, and with the side rooted to the bottom of the table, getting anything from this second trip to Liverpool in just over a week would prove hard.
He's Liverpool's figurehead in a bristling attacking unit, fitting Jurgen Klopp's style of play perfectly with his all-action mantra.
The Anfield club have been the embodiment of attacking flamboyance under their German manager, particularly this season with Roberto Firmino, Philippe Coutinho, Mohamed Salah and Sadio Mane making up their frightening front-four.