It was a tale of clinical finishing from the away side and an outstanding performance between the sticks for goalkeeper Pepe Reina.
Stewart Downing opened the scoring before Luis Suarez continued it, with two in the first half and his hat trick goal in the second.
Roberto Martinez started with the same side that beat Reading 3-0 last weekend and he almost had a dream start when Emmerson Boyce's cross was volleyed by Arouna Kone but not hard enough to beat Reina after just 40 seconds.
Instead it was Liverpool who scored early, with a long pass down the right finding Philippe Coutinho who crossed from the left and found Stewart Downing who had lost his marker Maynor Figueroa and headed past Ali Al Habsi after just three minutes.
Liverpool looked shaken when Latics' attacked but after 18 minutes they'd doubled their lead.
The Brazilian Coutinho was the man involved again as he was given space on the edge of the area to slot the ball between the defence and into the path of Suarez who beat the offside trap and slotted the ball beyond Al Habsi from close range.
Then came the series of Reina saves.
First it was Emmerson Boyce who tested him with a volley inside the area that looked destined for the top corner but, the Spanish stopper launched himself to his top corner to tip the ball away.
Jean Beausejour's out swinging corner was then met by the head of Gary Caldwell on half an hour but it was another top save, this time low and at the keeper's feet.
Despite showing promise and endeavour going forward Latics were caught again at the back, this time they conceded a free kick 25 yards out, with the dangerous Suarez lurking to take it.
An unfortunate deflection off Shaun Maloney took the ball just far enough away from Al Habsi's glove as he dove to his bottom left corner and tipped the ball onto the post and into the net.
On the stroke of half time it was a Beausejour free kick that looked to have surely brought Latics their goal but, Reina was at the ready again as he sprawled across to his top right corner and pushed the ball over the bar.
The second half was much steadier in general but Latics found themselves picking the ball out of the net again when Glen Johnson bullied his way through the defence and slipped Suarez in down the right.
The Uruguayan collected his hat trick by putting the ball between Al Habsi's legs from close range down the right of the six yard box.
Latics had more chances as the game went on and the bright spark of Callum McManaman gave Liverpool something to think about.
Liverpool slowed down their tempo towards the last 15 minutes and saw the game out at 4-0.