New signing Philippe Coutinho marked his Liverpool debut with a goal as an understrength Swansea side with one eye on a Wembley final next week put up little fight at Anfield.
The 20-year-old scored the important second goal moments after the break following Steven Gerrard's first-half penalty.
Jose Enrique, Luis Suarez and Daniel Sturridge, also from the spot, finished off the visitors who rarely looked interested in, or capable of, making a contest of it.
Brendan Rodgers, facing the club he left in the summer for the third time this season, began the week talking up what an important seven days lay ahead.
But after a home defeat to West Brom and one against Zenit St Petersburg in the Europa League this game took on even more significance.
It was a match Liverpool effectively could not afford to do anything but win, although that only served to paper over the cracks which have been exposed recently.
As emphatic as the scoreline was - incredibly securing a first win over a top...