4-0, min. 66, Firmino.
However, the floodgates opened for the Reds in the second half, as Firmino masterfully volleyed home a Coutinho free kick to double the advantage.
Then defender Alexander-Arnold surged into the box to finish emphatically, Firmino had his second a minute later, this time finishing from close range after unselfish play from Mohamed Salah, and Oxlade-Chamberlain completed the rout.
Less than two minutes later, Salah seized upon a awful Leroy For backpass to set up an easy tap-in For Firmino.
Coutinho needed just six minutes to conjure some typical magic when he curled the ball in from distance.
Liverpool, whose wretched defensive record cost them the Premier League title in 2013/14 after leaking 50 goals in 38 games, have conceded 23 times in 19 games so far this season. The Swans have registered just three wins so-far this season.
It was the Brazilian's fifth goal against Swansea in four appearances.
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Swansea had a good spell of possession but Liverpool never looked anxious defensively, and equally the home side were creating chances with Emre Can, Firminoand Salah at the other end.
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.
"First half, he helped left full-back to right full-back, he was everywhere".
Emre Can failed to test Fabianski after Kyle Naughton's misplaced pass created an opportunity for a second Liverpool goal, before Ragnar Klavan dived in to block a McBurnie strike at the other end as Swansea settled.
The goal was a big moment for the youngster, who had a stellar game and will look to push on and start more often over Joe Gomez in Nathaniel Clyne's absence this season.
Liverpool were comfortable but needed a second goal to put the match beyond their visitors and, after Salah had an attempt saved by Fabianski, Firmino latched on to a Coutinho free-kick over the top to volley beyond the Poland global.