Cesc Fabregas' early goal was enough to give Chelsea victory at the Liberty Stadium.
Swansea had their best chances to equalise in the final 15 minutes, with Andre Ayew hammering a shot wide before Kyle Naughton fired straight into the hands of Thibaut Courtois. After such a tiresome first half performance from Swansea, in the final moments of the game the Swans began to fight.
"Sometimes when you are in a dip of form and you are struggling to get points, to win whatever it takes, to do it is always positive".
Andy King's heavy touch gifted Chelsea possession and he was duly punished with Fabregas sweeping home from 20 yards for his 50th Premier League goal.
Despite facing an uphill battle in the Premier League the Italian boss has assured the Chelsea faithful that a top-four qualification is certainly on the cards.And the club will do everything to put up a fight until it's mathematically impossible.
The Blues are now fifth in the Premier League table but Liverpool's recent draws against West Brom and Stoke have given them a chance.
Palace, which looked destined for relegation after losing its opening seven fixtures without scoring a goal, has climbed to 11th place to sit six points clear of the bottom three, where only Southampton are capable of catching the south London club.
Congress appoints Kamal Nath as Madhya Pradesh state chief
The Congress on Thursday appointed senior leader Kamal Nath the chief of the Madhya Pradesh Congress Committee. He added there was no factionalism or division among the state leaders and the party was united in the state.
Asked about Ayew's challenge, Carvalhal said: "I don't want to (distract) too much from what we did with referee situations".
Tottenham play their game in hand against Watford on Monday.
They travel to Bournemouth next weekend before the Southampton and Stoke matches.
"We just have to keep on winning, but they obviously have the advantage because they are on top".
"We have had to dig in in certain moments and we are ready to do that".
"We must look to the games that we have - Bournemouth, Southampton and Stoke - and try to achieve the necessary points to stay in the division". "We will do our job", he explained.
Chelsea FC have three games to try and break back into the top four before the season is out.
Meanwhile, Swansea have lost consecutive league games for the first time under Carlos Carvalhal, last doing so in Paul Clement's final two games in charge in December.