Antonio Conte's Chelsea won for the 17th time in their last 20 league games to push them a step closer to the title. Cesc Fabregas, restored to the team in place of Nemanja Matic, was making his 300th Premier League appearance and the former Arsenal star marked the milestone in the 19th minute with his 46th goal in the competition.
Picked out inside the penalty area by Pedro's cut-back, Fabregas nimbly adjusted his stride before clipping his shot past Lukasz Fabianski.
Despite being out-played for much of the first half, Swansea snatched an equaliser seconds before the interval at Stamford Bridge.
Gylfi Sigurdsson's long free-kick caught the Blues napping and Spanish striker Fernando Llorente rose to head powerfully beyond Thibaut Courtois.
But Chelsea's dominance was rewarded in the 72nd minute when Pedro's routine long-range effort slipped past a weak attempted stop by Fabianski.
Chelsea's Pedro (R) scores their second goal
Reuters Diego Costa wrapped up the points when he finished off Eden Hazard's pass in the 84th minute for his 17th goal of the season.
While sacked boss Claudio Ranieri was saying his farewells at the club's Belvoir Drive training base on Saturday, Leicester's fight for survival took a turn for the worse without the players even kicking a ball.
Still digesting Ranieri's stunning dismissal on Thursday, Leicester don't play until Liverpool's visit to the King Power Stadium on Monday.
Amid reports a player revolt had led to Ranieri's exit, several Leicester players took to social media to praise the Italian, although none expressed disappointment at his exit.
But there was bad news for the malcontents from Selhurst Park, where Crystal Palace's 1-0 win over Middlesbrough left Leicester one point from safety in 18th place.
Palace had lost six of their last seven league games and their previous five league fixtures at Selhurst Park all ended in defeat.
But Sam Allardyce's side climbed above Leicester thanks to Patrick van Aanholt, who notched his first goal for Palace since his January move from Sunderland with a cool finish from the edge of the area in the 34th minute.
Middlesbrough are without a win in nine league games and lie one point above the bottom three.
Everton pushed their former manager David Moyes closer to relegation with a 2-0 win over bottom of the table Sunderland at Goodison Park.
Everton's Romelu Lukaku scores their second goal
Reuters Ronald Koeman's team went ahead when Senegal midfielder Idrissa Gueye fired into the roof of the net in the 40th minute.
Belgian striker Romelu Lukaku sealed the points for seventh placed Everton in the 80th minute to leave Sunderland three points from safety.
Hull missed a chance to climb out of the relegation zone with a 1-1 draw against Burnley at the KCOM Stadium.
Tom Hudderstone's 72nd minute penalty, awarded for Michael Keane's handball, put Marco Silva's second bottom team ahead.
But Burnley, embarrassedly beaten by non-league Lincoln in the FA Cup last weekend, equalised through Keane four minutes later.
The visitors held on for only their second away league point this season despite Ashley Barnes' late red card for elbowing Andrea Ranocchia.
Bournemouth are just five points above the relegation zone after losing 2-1 at West Bromwich Albion.
RESULTS:Chelsea 3 Fabregas 19, Pedro 72, Costa 84
Swansea City 1 Llorente 45+2
Crystal Palace 1 Patrick van Aanholt 34
Middlesbrough 0West Bromwich Albion 2 Dawson 10, McAuley 21
Bournemouth 1 Joshua King 4 (pen)
Hull City 1 Tom Huddlestone 72(pen)
Burnley 1 Michael Keane 76
Everton 2 Idrissa Gueye 40, Romelu Lukaku 80
Sunderland 0Standings P W D L F A
Pts1
Chelsea 26 20 3 3 55 19
632
Manchester City 25 16 4 5 51 29
523
Tottenham Hotspur 25 14 8 3 46 18
504
Arsenal 25 15 5 5 54 28
505
Liverpool 25 14 7 4 54 30
496
Manchester United 25 13 9 3 38 21
487
Everton 26 12 8 6 42 27
448
West Bromwich Albion 26 11 7 8 36 32
409
Stoke City 25 8 8 9 30 36
3210
West Ham United 25 9 5 11 34 43
3211
Burnley 26 9 4 13 28 37
3112
Southampton 25 8 6 11 28 31
3013
Watford 25 8 6 11 29 42
3014
Bournemouth 26 7 5 14 36 51
2615
Swansea City 26 7 3 16 32 57
2416
Middlesbrough 26 4 10 12 19 28
2217
Crystal Palace 26 6 4 16 33 46
2218
Leicester City 25 5 6 14 24 43
2119
Hull City 26 5 6 15 23 50
2120
Sunderland 26 5 4 17 24 48
19 
Chelsea's Pedro (R) scores their second goal Reuters Diego Costa wrapped up the points when he finished off Eden Hazard's pass in the 84th minute for his 17th goal of the season.
While sacked boss Claudio Ranieri was saying his farewells at the club's Belvoir Drive training base on Saturday, Leicester's fight for survival took a turn for the worse without the players even kicking a ball.
Still digesting Ranieri's stunning dismissal on Thursday, Leicester don't play until Liverpool's visit to the King Power Stadium on Monday.
Amid reports a player revolt had led to Ranieri's exit, several Leicester players took to social media to praise the Italian, although none expressed disappointment at his exit.
But there was bad news for the malcontents from Selhurst Park, where Crystal Palace's 1-0 win over Middlesbrough left Leicester one point from safety in 18th place.
Palace had lost six of their last seven league games and their previous five league fixtures at Selhurst Park all ended in defeat.
But Sam Allardyce's side climbed above Leicester thanks to Patrick van Aanholt, who notched his first goal for Palace since his January move from Sunderland with a cool finish from the edge of the area in the 34th minute.
Middlesbrough are without a win in nine league games and lie one point above the bottom three.
Everton pushed their former manager David Moyes closer to relegation with a 2-0 win over bottom of the table Sunderland at Goodison Park.
Everton's Romelu Lukaku scores their second goal Reuters Ronald Koeman's team went ahead when Senegal midfielder Idrissa Gueye fired into the roof of the net in the 40th minute.
Belgian striker Romelu Lukaku sealed the points for seventh placed Everton in the 80th minute to leave Sunderland three points from safety.
Hull missed a chance to climb out of the relegation zone with a 1-1 draw against Burnley at the KCOM Stadium.
Tom Hudderstone's 72nd minute penalty, awarded for Michael Keane's handball, put Marco Silva's second bottom team ahead.
But Burnley, embarrassedly beaten by non-league Lincoln in the FA Cup last weekend, equalised through Keane four minutes later.
The visitors held on for only their second away league point this season despite Ashley Barnes' late red card for elbowing Andrea Ranocchia.
Bournemouth are just five points above the relegation zone after losing 2-1 at West Bromwich Albion.RESULTS:Chelsea 3 Fabregas 19, Pedro 72, Costa 84 Swansea City 1 Llorente 45+2Crystal Palace 1 Patrick van Aanholt 34 Middlesbrough 0West Bromwich Albion 2 Dawson 10, McAuley 21 Bournemouth 1 Joshua King 4 (pen)Hull City 1 Tom Huddlestone 72(pen) Burnley 1 Michael Keane 76Everton 2 Idrissa Gueye 40, Romelu Lukaku 80 Sunderland 0Standings P W D L F A Pts1 Chelsea 26 20 3 3 55 19 632 Manchester City 25 16 4 5 51 29 523 Tottenham Hotspur 25 14 8 3 46 18 504 Arsenal 25 15 5 5 54 28 505 Liverpool 25 14 7 4 54 30 496 Manchester United 25 13 9 3 38 21 487 Everton 26 12 8 6 42 27 448 West Bromwich Albion 26 11 7 8 36 32 409 Stoke City 25 8 8 9 30 36 3210 West Ham United 25 9 5 11 34 43 3211 Burnley 26 9 4 13 28 37 3112 Southampton 25 8 6 11 28 31 3013 Watford 25 8 6 11 29 42 3014 Bournemouth 26 7 5 14 36 51 2615 Swansea City 26 7 3 16 32 57 2416 Middlesbrough 26 4 10 12 19 28 2217 Crystal Palace 26 6 4 16 33 46 2218 Leicester City 25 5 6 14 24 43 2119 Hull City 26 5 6 15 23 50 2120 Sunderland 26 5 4 17 24 48 19 