Tottenham's 5-2 win against Southampton earlier in the day – inspired by the hat-trick heroics of the record-breaking Harry Kane – had pushed Jurgen Klopp's men down to fifth.
The hosts took a while to find their stride at Anfield, but Swansea never looked capable of a repeat of their 3-2 win in this fixture last season.
Philippe Coutinho's stunner gave the hosts the lead early on, before Roberto Firmino, who scored two in that match in January, doubled the advantage seven minutes into the second half.
Trent Alexander-Arnold then netted his first Premier League goal in front of the Kop to put the match beyond Swansea and Firmino’s second made it 4-0 soon after.
Alex Oxlade-Chambelain added further gloss with his maiden home strike for Liverpool.
The result moves Liverpool a point clear of Spurs, while Swansea – still under the caretaker charge of Leon Britton following the sacking of Paul Clement last week – remain at the foot of the table and five points from safety.
Arriving at Anfield as the Premier League's bottom club, Swansea will not have welcomed the sight of three members of Liverpool's 'Fab Four' on the team sheet, and all of that trio were involved as the home side took the lead inside six minutes.
Jordan Ayew conceded possession to Firmino and, after the ball had been spread wide to Mohamed Salah, Coutinho stepped up to curl a magnificent finish beyond Lukasz Fabianski.
While Liverpool continued to have the better of the possession, Swansea showed occasional signs of addressing their own attacking problems.
The Welsh club, who handed striker Oli McBurnie his full Premier League debut, have averaged just two shots on target per match this season but had achieved that by the 20th minute on Merseyside.
Emre Can failed to test Fabianski after Kyle Naughton's misplaced pass created an opportunity for a second Liverpool goal, before Ragnar Klavan dived in to block a McBurnie strike at the other end as Swansea settled.
Soft penalty calls for a Tom Carroll tug on Salah were correctly ignored by referee Kevin Friend, but Liverpool squandered a subsequent glorious chance to double their lead when Firmino drilled wide with time to pick his spot.
Liverpool were comfortable but needed a second goal to put the match beyond their visitors and, after Salah had an attempt saved by Fabianski, Firmino latched on to a Coutinho free-kick over the top to volley beyond the Poland international.
Alexander-Arnold's milestone goal arrived when he charged into the Swansea box, latched on to an Alfie Mawson clearance and rifled a shot of the underside of the crossbar.
Firmino made it 4-0 a minute later – Leroy Fer's poor pass back into his own half was seized upon by Salah, who squared for his Brazilian colleague to tap home.
With the win already in the bag, Oxlade-Chamberlain made the most of some questionable Swansea defending in the box to unleash a shot that flew past Fabianski and opened his own Anfield account.
