Results near the bottom of the table, including wins for Southampton and West Bromwich Albion, meant Swansea were back in serious relegation trouble, while Chelsea's top four hopes were revived afer Liverpool were held by Stoke City.
In what was a slippery and sloppy clash, Cesc Fàbregas's early goal was enough for the Blues to escape the Liberty Stadium with all three points to put the pressure on fourth-placed Tottenham Hotspur.
Fàbregas strikes bright and early
In a must win game for both sides, it was the visitors who saw the first chance of the game, and they delightfully took it. Eden Hazard managed to pounce on a loose ball and find Fàbregas, who curled his effort pass one-time Arsenal team mate Lukas Fabianski. An early goal for Chelsea allowed them to dictate the remainder of the first half.
Due to the rain pouring down in Wales, the first half was full of players slipping on the ptich and poor first touches, making for a sloppy game of football. Chelsea almost went 2-0 up in the 22nd minutes after a bouncing ball, headed by Olivier Giroud, in the box was hacked away by Alfie Mawson, only for it to skim his own crossbar.
A first half with little to note from either side, apart from the well taken goal from Fàbregas.
Swansea wake up, but too late to snatch a point
The second half saw a continuation of sloppy play, but Swansea had clearly woken up after the break. An early chance fell to André Ayew, but his strong header flew over the bar. The home side controlled much of the second half action, but Chelsea again went close to making it 2-0 with 15 minutes left to play. More interplay between Fàbregas and Hazard eventually saw the ball fall to Victor Moses at the near post, but the wing-back couldn't scramble it inside the post.
Ayew then went close again with just over ten minutes remaining, but his fierce shot curled just wide of the post. Kyle Naughton then had his opportunity a minute later, but his shot was saved comfortably by goalkeeper Thibaut Courtois. The Swans continued to push for a late equaliser, and they almost got it as Tom Carroll struck his shot well from outside the box, but it flew wide of the post.
It had been a resilient second half performance from hosts Swansea, but it was too little too late as Fàbregas's early strike was in the end enough for Chelsea to escape a rainy day in Wales with all three points. The win leaves Chelsea in fifth, but just two points behind Tottenham, who play Watford on Monday night, in fourth place, although the Blues face a massive game agianst Liverpool next weekend. Swansea on the other hand are now just one point clear of the relegation zone, with three games remaining., starting with AFC Bournemouth away.