This was far from straightforward for Antonio Conte's side and had referee Neil Swarbrick awarded Swansea a penalty shortly before Pedro made it 2-1 then the outcome might have been different.
However, in the end Chelsea's sweeping forward play earned them a 10th straight home Premier League win as they took another significant step towards a second title in three seasons.
On a weekend when the first major silverware of the season - the EFL Cup - is handed out at Wembley, the Blues look unstoppable. They have 63 points from 26 games - three more than at the same stage in 2014-15 when last crowned champions of England.
Fabregas could have ended the game with four goals on his return to the side.
The Spain midfielder had a goal-bound shot deflected behind shortly before he opened the scoring, was denied by former Arsenal team-mate Lukasz Fabianski and also rattled the bar.
With former Blues midfielder Frank Lampard watching on, Chelsea turned on the style.
While it required an error from Fabianski to restore the lead, Eden Hazard's exquisite timing and pass for Costa to make it 3-1 was a delight.
Positives in defeat for Swansea
Chelsea were forced to work hard for three points thanks to a well organised and energetic Swansea side and the Swans looked a shadow of the team that was bottom of the Premier League table five weeks ago.
Their four-point safety cushion at the start of the day is down to three, but boss Paul Clement will have been pleased with the way his side frustrated the runaway leaders for long spells.
Llorente's equaliser shook Chelsea who were showing signs of frustration before Pedro made it 2-1.
Swansea's next four games - Burnley (home), Hull City (away), Bournemouth (away) and Middlesbrough (home) - give them a chance to stay clear of the bottom three before they entertain Tottenham on 4 April.
Man of the match - Cesc Fabregas (Chelsea)
'It was a clear handball' - what they said
Chelsea manager Antonio Conte:"We played very well, it was a good performance, and we created many chances to score. We conceded at the end of the first half, after the time was finished, so in this case there was a bit of luck, but we showed great character in the second half.
"We deserved a lot to win the game, now it's important to continue in this way."
Swansea City boss Paul Clement:"Any game we play and don't win we are disappointed. Chelsea are a very good side, they have fantastic quality and that was the difference. We didn't have a lot of chances but we came in at 1-1 for half-time and for long periods we defended really well.
"There was a big moment with the handball, I thought Cesar Azpilicueta handled it at 1-1, it's a clear handball. That gives you a chance to go 2-1 up but three minutes later you're 2-1 down with a soft goal. Based on chances they deserved to win, but there was big moment that didn't go our way, and who knows what might have happened."
Chelsea have nine days to prepare for their next game away to West Ham United on Monday, 6 March (20:00 GMT). Swansea entertain Burnley on Saturday, 4 March (15:00 GMT).