Luis Suarez netted a double after Raheem Sterling's opener as the Reds recorded their second 3-0 win in a row following Sunday's triumph at QPR to make it three victories from their past four outings.
Sterling made it a goal to the good for Liverpool inside 20 minutes when he raced onto Suarez's through ball to calmly lob over an advancing Simon Mignolet just seven minutes before Suarez doubled the advantage.
The Uruguayan netted the first of his brace when he received the ball from skipper Steven Gerrard before bouncing off Black Cats defender Carlos Cuellar prior to him racing into the area to beat Mignolet with the outside of his right foot.
Brendan Rodgers' men were then in cruise control and managed to wrap up proceedings eight minutes into the second half when Gerrard picked out Suarez from 60 yards away for the former Ajax star to fire home for his 15th goal in 19 outings this campaign.
Anfield, Liverpool - 44,228
Yellow cards:LIV - nil SUN - James McClean 60'