Andre Ayew's header and a sumptuous Jack Cork goal put the hosts in charge after a vibrant first-half display.
Christian Benteke nodded in to give the visitors hope, but Ayew's second goal swiftly ended those aspirations.
Brad Smith was then sent off for Liverpool, whose hopes of Champions League qualification now rest on winning the Europa League.
It is a victory which moves Swansea, who have two games remaining, to 13th in the table and opens an unassailable 11-point gap between them and third-from-bottom Sunderland.
With Liverpool playing their first league game since an inquest concluded the 96 fans who died in the Hillsborough disaster were unlawfully killed, the pre-match tributes at the Liberty Stadium made for a moving atmosphere.
Captains Martin Skrtel and Ashley Williams carry flowers out on the pitch in memory of the Hillsborough victims
On the pitch, Swansea were as impressive against Liverpool as they were abject in their 4-0 capitulation at Leicester in their previous outing.
With this match bookended by the two legs of their Europa League semi-final against Villarreal, Liverpool made eight changes as they named their youngest side of the Premier League era with an average age of 23.
This was not the first time Jurgen Klopp had selected an experimental team with European commitments in mind, as a similarly inexperienced line-up won comfortably at Bournemouth in April.
Liverpool fielded their youngest starting XI in the Premier League era with an average age of 23 years 218 days
However, against Swansea, Klopp's side unravelled as their youngsters were overwhelmed.
Midfielder Pedro Chirivella endured a torrid first league start, and the 18-year-old was replaced by the seasoned Lucas Leiva at half-time.
Chirivella's midfield colleague Kevin Stewart did not fare much better, while young left-back Smith was sent off after receiving two yellow cards.
Swansea were already all but guaranteed a sixth successive season in the Premier League, but knew a point against Liverpool would officially secure survival.
Soundly beaten by Leicester and Newcastle in their last two games, there was an onus on Francesco Guidolin's side to produce an improved performance - and they did so in style.
Cork embodied their dynamism with a thrusting display in midfield, crowned by his arcing shot from the edge of the penalty area which gave his side their second goal.
The Swans were given a fright when substitute Benteke headed in from a corner to halve Liverpool's deficit.
But the home side were never genuinely troubled and, two minutes later, Ayew fired into the bottom corner as Swansea scored three goals for the first time in the Premier League this season.