Things looked bleak for the Premier League's bottom side, still searching for their next manager after sacking Paul Clement last Wednesday, when Philippe Coutinho curled home a superb sixth-minute opener.
The hosts' sluggishness prevented Jurgen Klopp's scoring further until early in the second half when Roberto Firmino volleyed in Coutinho's free-kick before adding his second after Trent Alexander-Arnold drilled in a half-volley off the underside of the crossbar, with Alex Oxlade-Chamberlain firing in the fifth seven minutes from time.
It allowed Liverpool to regain fourth place after Tottenham's victory earlier in the day but left Swansea five points from safety after a seventh successive away defeat.
Klopp said, "It's quite difficult, you can say a lot before the game in the analysis but it's always different to see it in the game. Swansea is a different team to play against, they play real football so our main tool or weapon should have been today counter-pressing because you cannot come through with all the balls but very often if you lose the ball and then the next second it's 80 yards away, but Swansea is playing football.
"Our timing was not good in the situations, our formation was not good in these situations [in the first half] and so we were always a bit too late and they could play. They didn't get a lot of chances to be honest, they had one or two half-chances but it was quite intense so the way was always really long to come back into the right positions, the right situations."