The Swans' relegation fears grew following a 1-0 defeat to Chelsea despite their brave performance with ten men for the majority of this game.
The Swans' hopes were severely dented by Chico Flores' dismissal after just 16 minutes, with referee Phil Dowd showing him his second yellow card following a four on Andre Schurrle.
Despite their numerical disadvantage, the Swans remained on level terms going into the break, but Chelsea finally broke the deadlock on 68 minutes.
Nemanja Matic's pass found Demba Ba, and the striker's shot squirmed under Michel Vorm.
The Swans continued to bravely battle away, but they just couldn't find a way through as Chelsea celebrated their first win at the Liberty.
Defeat left the Swans on 33 points and just three points off third-bottom Fulham with four games to go.
The Swans made two changes to the starting XI.
From the side that lost at Hull last time out, Pablo Hernandez came in for Michu as the Spanish international missed out with a sore calf.
The other change to Garry Monk's side saw Nathan Dyer start on the right wing in place of Jonathan de Guzman, who dropped to the bench.
Also included on the bench was 20-year-old midfielder Jay Fulton, who was involved in the matchday squad for the first time since arriving from Falkirk in January.
SWANS:Michel Vorm, Angel Rangel, Chico Flores (Jordi Amat, 19), Ashley Williams (capt), Ben Davies, Leon Britton (Jonathan de Guzman, 86), Jonjo Shelvey, Pablo Hernandez, Nathan Dyer (David Ngog, 73), Wayne Routledge, Wilfried Bony.
SUBS: Gerhard Tremmel, Neil Taylor, Jay Fulton, Marvin Emnes.
CHELSEA: Petr Cech, Branislav Ivanovic, John Terry (capt), Gary Cahill, Cesar Azpilicueta, Willian, Nemanja Matic, Ramires (Oscar, ht), Mohamed Salah, Andre Schurrle (Samuel Eto'o, ht), Demba Ba (John Obi Mikel, 79).
SUBS: Mark Schwarzer, Ashley Cole, David Luiz, Fernando Torres.
Before the game got underway both clubs paid respect to the 96 fans who had lost their lives in the Hillsborough disaster 25 years ago, while they also paid tribute to 15-year James Lock, who passed away earlier in the week.
Both sides started brightly, but it was Chelsea who carved open the first big opportunity of the game after just six minutes, with Branislav Ivanovic's cross finding Mohamed Salah, but he guided his shot inches wide from 12 yards out.
The Swans hit back via Wilfried Bony, who leapt to meet Angel Rangel's early cross which Petr Cech had to tip it over the crossbar for a corner.
But the hosts were dealt a major blow after 16 minutes as Chico Flores, who had been booked minutes earlier, was again booked by referee Phil Dowd for a challenge on Andre Schurrle just outside the box.
It forced Garry Monk into an early change as Jordi Amat replaced Pablo Hernandez to ensure the Swans returned to four at the back.
Chelsea were enjoying the better of possession and territory, with the Swans sitting back and looking for the counter attack.
And Jonjo Shelvey ensured Cech was staying alert as his attempted 40-yard chip was collected by the Czech keeper.
Willian then curled his 25-yard shot high and wide before Rangel got an important touch to stop Ramires as he was entering the box.
Chelsea kept plugging away and Branislav Ivanovic headed over from a soft corner the Swans had conceded as they failed to clear their lines.
But the Swans, too, were showing a willingness to break in numbers and when Bony, Wayne Routledge and Leon Britton all linked up to find Nathan Dyer, the winger's rasping shot was padded wide for a corner by Cech.
Then, with seconds left, Salah again wasted a huge opportunity as he latched onto Ramires pass inside the box before firing high into the Jack Army behind Vorm's goal.
That was the end of a dramatic first half, but the Swans would go into the break happy with their response after the early red card.
HALF-TIME: Swans 0 Chelsea 0
Jose Mourinho made a double change at the break with Oscar and Samuel Eto'o replacing Ramires and Schurrle.
It was an attacking move by the Chelsea boss, who looked for his side to push on and get themselves ahead.
And they went close to doing that in the 56th minute as Ivanovic's cross was flicked on by Demba Ba, but Vorm watched it bounce inches wide.
Then substitute Eto'o was dealt a massive chance to fire Chelsea ahead as Ashley Williams' clearance deflected off the striker and into his path but he scuffed wide from just eight yards.
Eto'o was again denied shortly after by a fantastic sliding challenge from Williams, but when the loose dropped to Ba the striker hit his shot on the turn but Vorm easily collected.
But the Swans hit Chelsea on the break from the following move as Routledge raced on from inside his own half. And when the winger fired his low shot, it deflected off the shoulder of John Terry and wide for a corner.
Shelvey's delivery was met by Bony, but his header flashed wide of the far post.
But Chelsea would be kept out no longer.
With 68 minutes on the clock, Nemanja Matic's ball forward found Ba, and when he fired low it squirmed under Vorm and into the net.
Monk responded by sending David Ngog on in place of Dyer as they went in search of a equaliser.
Ba then fired high and wide in what was his final act of the day as Mourinho send on defensive midfielder John Obi Mikel in his place.
Chelsea, though, continued to look for a second goal and Eto'o drove wide after being teed up by Salah.
Monk made his final change with four minutes to go as Jonathan de Guzman replaced Leon Britton.
The Swans pushed for an equaliser, but they just couldn't break down a solid Chelsea side, who moved second after this victory.