The Blues reduced the gap between them and fourth placed Tottenham Hotspur who host Watford at the Wembley Stadium on Monday to two points.
If Swansea should be losing hope after six Premier League games without a win, nobody has told them.
If Fabregas had felt that his former manager would want him to work hard in the middle of the park, Conte would demand even more, which made Cesc's desire to be a success at Chelsea even more. The south London club climbed to 11th place - six points clear of the bottom three - after beating Leicester 5-0.
"We dominated and created many chances but we scored only one goal, and in the final Swansea had the chance to draw".
A seventh home loss of the season, though, coupled with wins for relegation rivals Crystal Palace, Southampton and West Bromwich Albion, has left Huddersfield three points above the drop zone.
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Chelsea controlled the first half, with Eden Hazard impressing, and might have put the game out of sight before the interval. Swansea's willingness and urgency looked pitiful for a team fighting relegation, and the sides went in at the break with Chelsea in full control. Now we have three games to go and have to win for our fans, for our work and then we'll see what happens.
"We just have to keep winning".
The Swans started to grow into the game towards the end of the half, but were unable to penetrate the Chelsea backline and test Thibaut Courtois.
With results elsewhere in the Premier League putting the pressure on the home side, Carlos Carvalhal had to upset the odds to ease the pressure on his team, as we approach the finale of throes of the season.
"If when I came here I said we will compete in the last three games to stay up, nobody would have believed me".
After a trip to Bournemouth on Saturday, fellow endangered sides Southampton and Stoke cross the border and both can expect to be met by a wall of noise and fight.