Cesc Fabregas marked his 300th Premier League appearance by firing the Blues ahead, poking the ball through the legs of Jack Cork and into the net.
The hosts were stunned when Swansea equalised from their first serious attempt on target on the stroke of half-time - Fernando Llorente heading in Gylfi Sigurdsson's free-kick.
Fabregas hit the bar before Pedro's curling effort restored the lead and Diego Costa netted the third from close range.
Swansea were denied a penalty when Cesar Azpilicueta handled inside the area at 1-1.
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.
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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.
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.
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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.
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."
Former England midfielder Jermaine Jenas: "I don't think Swansea should have had a penalty as the distance from Gylfi Sigurdsson to Cesar Azpilicueta is too close and Azpilicueta's arm is already out. His hand is there because he's trying to stop Sigurdsson's run."
Ex-England captain Alan Shearer: "I think it was a penalty. I think it was a deliberate movement of his hand towards the ball and I think Chelsea got away with one there. It could have been very different if the ref had given it.
"We've seen in recent weeks with Swansea that they made it very difficult for Liverpool at Anfield, they were unlucky to lose at Manchester City. They are very organised. The difference between Liverpool and City with this Chelsea side is the pace with which they go forward. That's why Cesc Fabregas was in the team today. He was brilliant. He's the one that started the goal off.
"It's topical that players are not working for mangers. The irony is last season we were sat here with a large bunch of these same Chelsea players - they weren't working for their manager and we know what happened. It's such a transformation now. We saw how brilliant they were with the ball but look at them now without it. The transformation from then to now is incredible."
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).
Match ends, Chelsea 3, Swansea City 1.
Second Half ends, Chelsea 3, Swansea City 1.
Attempt missed. Cesc Fàbregas (Chelsea) right footed shot from outside the box is too high. Assisted by Willian.
Foul by N'Golo Kanté (Chelsea).
Jack Cork (Swansea City) wins a free kick in the defensive half.
Corner,  Chelsea. Conceded by Alfie Mawson.
Kurt Zouma (Chelsea) wins a free kick in the defensive half.
Foul by Fernando Llorente (Swansea City).
Substitution, Chelsea. Willian replaces Eden Hazard.
Substitution, Chelsea. Kurt Zouma replaces Victor Moses.
Goal!  Chelsea 3, Swansea City 1. Diego Costa (Chelsea) left footed shot from the centre of the box to the bottom left corner. Assisted by Eden Hazard.
Attempt missed. N'Golo Kanté (Chelsea) right footed shot from the centre of the box is too high. Assisted by Nemanja Matic.
Substitution, Swansea City. Luciano Narsingh replaces Wayne Routledge.
Leroy Fer (Swansea City) is shown the yellow card for a bad foul.
Eden Hazard (Chelsea) wins a free kick in the attacking half.
Foul by Leroy Fer (Swansea City).
Foul by Victor Moses (Chelsea).
Martin Olsson (Swansea City) wins a free kick in the defensive half.
Attempt saved. Gylfi Sigurdsson (Swansea City) right footed shot from outside the box is saved in the top centre of the goal.
Substitution, Swansea City. Jordan Ayew replaces Tom Carroll.
Substitution, Chelsea. Nemanja Matic replaces Pedro.
David Luiz (Chelsea) is shown the yellow card for a bad foul.
Foul by David Luiz (Chelsea).
Fernando Llorente (Swansea City) wins a free kick in the attacking half.
Gary Cahill (Chelsea) wins a free kick in the defensive half.
Foul by Wayne Routledge (Swansea City).
Goal!  Chelsea 2, Swansea City 1. Pedro (Chelsea) left footed shot from outside the box to the bottom left corner. Assisted by Cesc Fàbregas.
Victor Moses (Chelsea) wins a free kick in the defensive half.
Foul by Fernando Llorente (Swansea City).
Foul by Diego Costa (Chelsea).
Alfie Mawson (Swansea City) wins a free kick in the defensive half.
Foul by Gary Cahill (Chelsea).
Leroy Fer (Swansea City) wins a free kick in the defensive half.
Pedro (Chelsea) wins a free kick in the defensive half.
Foul by Jack Cork (Swansea City).
Corner,  Chelsea. Conceded by Kyle Naughton.
Attempt blocked. N'Golo Kanté (Chelsea) right footed shot from outside the box is blocked. Assisted by Gary Cahill.
Foul by Diego Costa (Chelsea).
Federico Fernández (Swansea City) wins a free kick in the defensive half.
Attempt blocked. Diego Costa (Chelsea) right footed shot from outside the box is blocked. Assisted by Cesc Fàbregas.
Chelsea stretched their lead at the top of the Premier League table to 11 points after victory over battling Swansea City at Stamford Bridge.