Willian's goal was his first in the Premier League since scoring in the 4-0 away win at Burnley on 28 October
Chelsea moved one point behind third-placed Tottenham with a victory over a Newcastle side who are now in the relegation zone.
Pedro gave the Blues an eighth-minute lead when he collected David Luiz's ball over the top, took a touch, then shot past Martin Dubravka.
But Newcastle equalised through Ciaran Clark's powerful header when he got between Antonio Rudiger and David Luiz from Matt Ritchie's corner.
Willian won it for Chelsea in the second half with a fine curling finish after being played in by Eden Hazard.
The result leaves Maurizio Sarri's side fourth, six points clear of Arsenal, who they face at Emirates Stadium in their next game on 19 January.
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Sarri's side do enough for the three points
Chelsea had failed to score in their previous two league matches at Stamford Bridge - a 1-0 loss to Leicester and a goalless draw with Southampton - but they netted early on with Pedro's seventh goal of the season in all competitions.
However, with Eden Hazard again featuring as a 'false nine' with Olivier Giroud on the bench and Alvaro Morata injured, they struggled to create further clear-cut chances before Clark equalised five minutes before the break.
There were boos heard inside Stamford Bridge at half-time, but Sarri's side were greatly improved in the second half, with Hazard a much more prominent threat.
The Belgian led Chelsea's attack, which resulted in their second goal as he ran at the Newcastle defence, offloaded to Willian who, from a tight angle, cut inside onto his right foot and curled a beautiful effort past Dubravka with the ball going in off the post.
With nine minutes left, 18-year-old Callum Hudson-Odoi, the subject of a £35m bid from German champions Bayern Munich, came on for only his second Premier League appearance.
The home fans chanted "we want you to stay" in the direction of the talented winger, who was part of England's Under-17 World Cup triumph in 2017 and has 18 months left on his current Chelsea deal.
Newcastle drop into the bottom three
Newcastle started the day 15th in the Premier League, but wins for Burnley and Southampton - along with Cardiff drawing - leaves Rafael Benitez's side in the bottom three.
Benitez won the manager of the month award in November, but since then they have only won one match in 10 in all competitions.
With the Spaniard unlikely to be given any money to make further signings - amid ongoing uncertainty about a possible takeover - there are real concerns that the club could drop into the second tier after only two seasons back in the top flight.
Before the game, Benitez said that the club's "reality" was "having to compete in a division when we cannot compete against Bournemouth, who are spending money".
At Stamford Bridge, Newcastle had late chances to snatch a point, but Ritchie shot over the bar and Salomon Rondon headed a chance wide.
Newcastle face a hugely important home game against Cardiff in their next league match, before tough assignments against Manchester City and Tottenham.
Another Newcastle failure against a top-six side - the stats
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Chelsea have only lost one of their 12 Premier League matches at Stamford Bridge this season, drawing four and winning the other seven.
Newcastle's total of 18 points from their opening 22 matches is their lowest tally at this stage of a top-flight season since 1988-89 campaign (17 points), with the Magpies going on to be relegated under manager Jim Smith.
Chelsea (played four, won three and drew one) are on their longest unbeaten league run since losing none of their opening 12 league games under manager Maurizio Sarri (played 12, won eight and drew four).
Newcastle have now lost 10 straight top-flight matches away from home against sides starting the day in the top four, last winning such a match back in November 2010 against Arsenal (played 26, won none, drew three, lost 23 since).
Rafael Benitez has now lost six of his eight away league games against former employers Chelsea in the Premier League (won one, drew one), including his two as Newcastle boss.
Chelsea's Eden Hazard has both scored (10) and assisted (10) at least 10 goals in league games this season - the only other player within the top five European Leagues to have also done so in 2018-19 is Barcelona's Lionel Messi (16 goals, 10 assists).
Pedro has now scored three goals in his two Premier League starts against Newcastle at Stamford Bridge - against no other side in the competition has the Spaniard netted more goals for Chelsea (three, level with Bournemouth).
Of players with at least 10 Premier League goals, only Ugo Ehiogu (84%) and David Wetherall (87%) have scored a higher percentage of their goals via their head than Newcastle's Kieran Clark (83%).
More to follow.
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Line-ups
Match Stats
Live Text
Line-ups
Chelsea
1Arrizabalaga
28Azpilicueta
2Rüdiger
30David Luiz
3Alonso
7Kanté
5JorginhoBooked at 63mins
17KovacicSubstituted forBarkleyat 63'minutes
11PedroSubstituted forHudson-Odoiat 81'minutes
10E HazardSubstituted forGiroudat 87'minutes
22Willian
Substitutes
8Barkley
13Caballero
18Giroud
20Hudson-Odoi
27Christensen
33Emerson
44Ampadu
Newcastle
12Dubravka
22YedlinSubstituted forManquilloat 82'minutes
20Lejeune
6Lascelles
2Clark
11RitchieBooked at 24mins
17PérezSubstituted forMurphyat 82'minutes
36Longstaff
14Hayden
30Atsu
9Rondón
Substitutes
5Schär
7Murphy
18Fernandez
19Manquillo
21Joselu
25Sterry
41Woodman
Referee:
Chris Kavanagh
Attendance:
40,491
Match Stats
Home TeamChelseaAway TeamNewcastle
Possession
Home66%
Away34%
Shots
Home10
Away9
Shots on Target
Home6
Away2
Corners
Home8
Away5
Fouls
Home6
Away13
Live Text
Posted at
Match ends, Chelsea 2, Newcastle United 1.
Full TimePosted at 90'+5'
Second Half ends, Chelsea 2, Newcastle United 1.
Posted at 90'+4'
Corner, Newcastle United. Conceded by David Luiz.
Posted at 90'+4'
Attempt blocked. Sean Longstaff (Newcastle United) right footed shot from the right side of the box is blocked. Assisted by Javier Manquillo.
Posted at 90'+2'
Offside, Chelsea. Marcos Alonso tries a through ball, but Willian is caught offside.
Posted at 90'+1'
Jorginho (Chelsea) wins a free kick on the right wing.
Posted at 90'+1'
Foul by Sean Longstaff (Newcastle United).
Posted at 90'+1'
Corner, Chelsea. Conceded by Javier Manquillo.
Posted at 88'
Callum Hudson-Odoi (Chelsea) wins a free kick on the right wing.
Posted at 88'
Foul by Christian Atsu (Newcastle United).
SubstitutionPosted at 87'
Substitution, Chelsea. Olivier Giroud replaces Eden Hazard.
Posted at 86'
Attempt missed. Salomón Rondón (Newcastle United) header from the centre of the box is close, but misses to the left. Assisted by Javier Manquillo with a cross.
Posted at 85'
Offside, Chelsea. Jorginho tries a through ball, but Callum Hudson-Odoi is caught offside.
SubstitutionPosted at 82'
Substitution, Newcastle United. Javier Manquillo replaces DeAndre Yedlin.
SubstitutionPosted at 82'
Substitution, Newcastle United. Jacob Murphy replaces Ayoze Pérez.
Posted at 81'
Attempt missed. Matt Ritchie (Newcastle United) right footed shot from the left side of the box is too high. Assisted by DeAndre Yedlin with a cross.
SubstitutionPosted at 81'
Substitution, Chelsea. Callum Hudson-Odoi replaces Pedro.
Posted at 79'
Corner, Newcastle United. Conceded by César Azpilicueta.
Posted at 77'
Delay over. They are ready to continue.
Posted at 75'
Delay in match David Luiz (Chelsea) because of an injury.
Posted at 75'
David Luiz (Chelsea) wins a free kick in the defensive half.
Posted at 75'
Foul by Ayoze Pérez (Newcastle United).
Posted at 75'
Offside, Chelsea. David Luiz tries a through ball, but Pedro is caught offside.
Posted at 73'
Attempt missed. David Luiz (Chelsea) right footed shot from outside the box is high and wide to the left from a direct free kick.
Posted at 72'
Marcos Alonso (Chelsea) wins a free kick in the attacking half.
Posted at 72'
Foul by Ayoze Pérez (Newcastle United).
Posted at 72'
Marcos Alonso (Chelsea) wins a free kick in the attacking half.
Posted at 72'
Foul by DeAndre Yedlin (Newcastle United).
Posted at 67'
David Luiz (Chelsea) wins a free kick in the defensive half.
Posted at 67'
Foul by Ayoze Pérez (Newcastle United).
Posted at 67'
Delay over. They are ready to continue.
Posted at 66'
Delay in match Jamaal Lascelles (Newcastle United) because of an injury.
Posted at 64'
Corner, Chelsea. Conceded by Jamaal Lascelles.
Posted at 64'
Attempt saved. Willian (Chelsea) right footed shot from the left side of the box is saved in the bottom left corner. Assisted by David Luiz with a through ball.
SubstitutionPosted at 63'
Substitution, Chelsea. Ross Barkley replaces Mateo Kovacic.
BookingPosted at 63'
Jorginho (Chelsea) is shown the yellow card for a bad foul.
Posted at 63'
Foul by Jorginho (Chelsea).
Posted at 63'
Salomón Rondón (Newcastle United) wins a free kick in the defensive half.
Posted at 58'
Offside, Chelsea. Pedro tries a through ball, but Eden Hazard is caught offside.
Goal!Posted at 57'
Goal! Chelsea 2, Newcastle United 1. Willian (Chelsea) right footed shot from the left side of the box to the top right corner. Assisted by Eden Hazard.
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Source: bbc.com