The Swans went down to a second consecutive league defeat as Chelsea claimed victory at Stamford Bridge on Boxing Day.
Eden Hazard's 29th minute strike proved the difference as the Blues kept the pressure on leaders Arsenal, while the Swans suffered back-to-back defeats following the narrow loss to Everton.
A busy first half of action saw Gerhard Tremmel deny Samuel Eto'o on a few occasions while skipper Ashley Williams also made a number of timely interceptions and clearances.
But Belgian international Hazard broke the deadlock just before the half-hour as he cut inside from the left and blasted a dipping shot below Tremmel.
In the second half, the Swans looked brighter and enjoyed better possession and territory, but they failed to create many chances.
There was a late surge of pressure from Michael Laudrup's side, but Chelsea held strong to claim victory.
It left the Swans on 20 points from 18 games, with the next fixture against Aston Villa in two days' time.
The Swans made six changes to the starting XI.
Michael Laudrup welcomed back Angel Rangel from suspension while Neil Taylor took up the other full-back role. Jordi Amat also started in defence in place of fellow countryman Chico Flores, who was on the bench.
Leon Britton and Alejandro Pozuelo were the changes in midfield while Alvaro Vazquez led the line as club record signing Wilfried Bony was among the substitutes.
The Swans were without Michel Vorm, Nathan Dyer and Michu through injury.
CHELSEA:Petr Cech, Branislav Ivanovic, David Luiz, John Terry (c), Ashley Cole, Ramires, John Obi Mikel, Juan Mata (Andre Schurrle, 72), Oscar (Frank Lampard, 67), Eden Hazard (Willian, 82), Samuel Eto’o.
SUBS: Mark Schwarzer, Cesar Azpilicueta, Gary Cahill, Fernando Torres.
SWANS: Gerhard Tremmel, Angel Rangel, Jordi Amat, Ashley Williams (capt), Neil Taylor, Jose Canas (Jonathan de Guzman, 61), Leon Britton, Jonjo Shelvey, Alejandro Pozuelo (Pablo Hernandez, ht), Wayne Routledge (Wilfried Bony, 76), Alvaro Vazquez.
SUBS: Gregor Zabret, Chico Flores, Ben Davies, Roland Lamah.
Both sides eased themselves into the game with a couple of early chances each.
Oscar was denied by a last-gasp clearance from Neil Taylor following an Eden Hazard through ball while Ashley Williams reacted quickly to deflect Branislav Ivanovic's shot over for a corner.
Hazard then scuffed his shot wide from an acute angle while Gerhard Tremmel comfortably dealt with a low Samuel Eto'o shot before later tipping a John Terry volley over the crossbar.
At the other end, Jordi Amat headed a Jonjo Shelvey free-kick while the latter drove a powerful effort just wide following a swift counter attack.
Chelsea, though, started to pile on the pressure and it was Williams who again came to the rescue.
After Terry touched a deep cross back along the face of goal, the Swans skipper just managed to clear as Eto'o was lurking just four yards out.
Then, with 29 minutes on the clock, Chelsea got their lead.
With the Swans looking to counter, Alvaro Vazquez's pass was cut out by Ashley Cole, and when he fed Hazard down the left, the Belgian raced on and cut inside before his powerful dipping shot creeped under Tremmel and into the net.
The hosts went close to doubling their lead soon after as Tremmel's attempted pass hit Eto'o, but the keeper recovered the loose ball as Oscar closed in.
The Swans needed a reaction and they got one when Shelvey flicked on a cross with the ball dropping to Vazquez, but the Spaniard's rising half-volley was tipped over by Petr Cech.
Shelvey's 30-yard free-kick then failed to trouble Cech before Juan Mata's curling shot dropped harmlessy wide.
Tremmel then had to be alert to deny Eto'o after the striker was found by a neat cross from Mata, with the German keeper reacting well to palm his initial effort before recovering the loose ball.
HALF-TIME: Chelsea 1 Swans 0
Michael Laudrup made a change at the break as Pablo Hernandez replaced fellow countryman Alejandro Pozuelo.
But the Swans were immediately under immense pressure as after just 13 seconds, Tremmel denied Eto'o from six yards following an excellent cross from Mata.
Eto'o was at it again four minutes later, but he scuffed a low shot wide from 20 yards with Tremmel at full stretch.
The Swans made another substitution as Jonathan de Guzman came on in place of Jose Canas on the hour mark.
The visitors were enjoying more time in the Chelsea half, but it was the Blues who were creating the better chances, and Tremmel again came to the rescue as he dived low to palm sub Frank Lampard's shot wide for a corner.
Laudrup made his final change with 15 minutes left as Wilfried Bony replaced Wayne Routledge, which meant Vazquez moved to the left wing.
And the Ivorian was soon into the action as he glanced an Angel Rangel cross wide inside a crowded box as the Swans pushed for an equaliser in the last few minutes.
But it never came as Chelsea held on to claim victory.