Victory saw Liverpool leapfrog Swansea into seventh spot and give former Swans manager Brendan Rodgers something to smile about at the end of a week that saw defeats by West Brom and then Zenit St Petersburg in the Europa League.
A penalty from Steven Gerrard got them on their way and three goals early in the second-half from impressive debutant Philippe Coutinho, Jose Enrique and Luis Suarez wrapped up the points against a side seemingly distracted by the League Cup final with Bradford next Sunday.
Daniel Sturridge, who like Coutinho missed the Europa League match, added a fifth from the penalty spot.
Swansea manager Michael Laudrup was made to regret sending out a starting line-up shorn of several first choice players, including leading scorer Michu, preferring to give the 15-goal Spaniard time on the bench.
Liverpool, who in three previous Premier League meetings with Swansea had failed to score, made all the running from the kick-off with Suarez looking particularly sharp, going close first with a freekick and then another good effort, which crept over the bar.