Ten-man Arsenal missed the chance to go top of the Premier League as Diego Costa's winner gave Chelsea victory at the Emirates Stadium.
The Gunners never fully recovered from defender Per Mertesacker's 18th-minute red card, awarded by referee Mark Clattenburg after he hauled down Costa as the striker raced clear.
The revitalised Costa scored the decisive goal five minutes later, turning in Branislav Ivanovic's cross at the near post to make it nine Premier League games without defeat for Chelsea against Arsenal.
Arsenal's potency suffered after manager Arsene Wenger decided to replace striker Olivier Giroud and introduce defender Gabriel to compensate for Mertesacker's dismissal.
Victory would have put Arsenal back on top but Chelsea survived in relative comfort to leave the Gunners in third place with Leicester City now holding a three-point lead over Manchester City at the Premier League summit.
Arsenal suffer pure frustration
This was the day Arsenal were meant to lay the ghost of Chelsea, who went into this game unbeaten in their last eight Premier League games against the Gunners.
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Even Wenger's bogey man, Jose Mourinho, was out of the picture after his sacking. Wenger has lost five and drawn six of eleven league meetings with his old adversary.
And yet it was the same old story for Arsenal as the frustration of their players and fans inside the Emirates reached boiling point long before the final whistle.
There was no shortage of spirit and endeavour from Arsenal in the face of the numerical disadvantage inflicted on them after Mertesacker's early red card.
If anything, it was inspiration and a little self-belief Arsenal lacked against a side that looked physically stronger in a game where Wenger's side was missing a warrior who could get in and among the visitors in those exchanges.
Their best effort of the match fell to Mathieu Flamini who attempted to convert Aaron Ramsey's through-ball with a kung-fu kick, where a header might have been more appropriate.
The result is hardly a terminal blow to Arsenal's ambitions but a wound inflicted in familiar fashion. It now remains to be seen how much of an after-effect there is.
Costa revival sparks Chelsea
Diego Costa suffered the abuse of Chelsea's fans in the aftermath of Jose Mourinho's sacking as they regarded his poor form and attitude as a key factor in the sacking of "The Special One".
The relationship is repaired now, with Costa regaining that mixture of marksmanship and menace that made him so significant in last season's Premier League title win.
Costa's near-post finish from Ivanovic's delivery was his sixth in eight games since Mourinho left - and it was not just that quality that helped Chelsea look much more like their old selves.
He got under the skin of Arsenal's players and fans, although he could hardly be blamed for his involvement in Mertesacker's red card when he was unceremoniously bundled over as he tried to race clear.
Costa departed to the resounding jeers of Arsenal's fans and cheers of Chelsea's supporters when he was replaced by Loic Remy after 68 minutes - job done and proof Hiddink's side are so much more effective when the Premier League's pantomime villain is on song.
Sanchez key to Arsenal title hopes
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Having talked about the lack of warriors in Arsenal's line-up, one look at Alexis Sanchez back in action shows how he can fit the bill.
The huge roar that swirled around the Emirates when he emerged after 57 minutes to replace Joel Campbell was not simply out of a growing desperation as Arsenal struggled against Chelsea - it was a signal that so much of the rest of the Gunners' season rests on the shoulders of the world-class Chilean.
It was his first appearance since sustaining a hamstring injury at Norwich City on 29 November and it was understandable he looked a little rusty, but the strength, perseverance and sheer force of will to influence a game were still in evidence in this cameo.
This was a major setback for Arsenal's title hopes - but the return of Sanchez confirms all is not lost if they keep him fit.
Man of the match - Willian (Chelsea)
The stats you need to know
Arsenal have now gone nine hours and 32 minutes without a Premier League goal against Chelsea
Chelsea are unbeaten in nine Premier League meetings with Arsenal (W6 D3)
Costa has scored six goals in six games under Guus Hiddink (all competitions)
Chelsea have won back-to-back Premier League away games for the first time this season
The Blues are on the current longest unbeaten run in the Premier League (W3 D4)
The Gunners have failed to score in consecutive league games for the first time since August 2012
What next?
The Gunners are at home to Burnley in the FA Cup next weekend, and the Blues are away at the MK Dons in the same competition.
Lineup, Bookings (5) & Substitutions (5) Arsenal 33 Cech
24 Bellerín
04 Mertesacker Dismissed
06 Koscielny
18 Monreal
20 Flamini Booked
16 Ramsey
28 Campbell (Sánchez - 57' )
(Sánchez - 57' ) 11 Özil
14 Walcott (Oxlade-Chamberlain - 75' )
(Oxlade-Chamberlain - 75' ) 12 Giroud (Gabriel - 22' ) Substitutes 03 Gibbs
05 Gabriel
13 Ospina
15 Oxlade-Chamberlain
17 Sánchez
21 Chambers
35 Elneny Chelsea 13 Courtois
02 Ivanovic
05 Zouma
26 Terry
28 Azpilicueta
12 Mikel Booked
21 Matic Booked
22 Willian
04 Fàbregas
08 Oscar Booked (Hazard - 77' )
(Hazard - 77' ) 19 Diego Costa (Remy - 68' ) Substitutes 01 Begovic
06 Baba
10 Hazard
14 Traore
18 Remy
24 Cahill
36 Loftus-Cheek Ref: Mark Clattenburg Att: 60,072
Diego Costa aus Brasilien

 Am 24. Januar besiegte der in London beheimatete Fußball-Club FC Chelsea den Stadtrivalen FC Arsenal mit 1:0 im Auswärtsspiel. Der FC Arsenal spielte nur noch mit 10 Männern in der 18. Minute, nachdem Per Mertesacker die Rote Karte bekommen hatte. Es gab im Spiel vier Gelbe Karten und insgesamt 27 Fouls. Diego Costa erzielte in der 23. Minute das einzige Tor. Mathieu Flamini vom FC Arsenal bekam danach die Gelbe Karte für ein Foul angezeigt. In der 60. Minute wurde Nemanja Matić die Gelbe Karte gezeigt. Costa wurde während des Spiels verletzt und Loïc Rémy ersetzte ihn in der 68. Minute. John Obi Mikel bekam in der 72. Minute die Gelbe Karte.

Das Spiel zwischen FC Chelsea und FC Watford am 3. Februar endete 0:0. Hier bekam Costas Kontrahent Sebastian Prödl die Gelbe Karte. Im Spiel gegen Manchester United am 7. Februar schoss Costa das einzige Tor zum Ausgleich mit 1:1 in der 90. Minute. Insgesamt hat der Brasilianer im Jahre 2016 bisher fünf Tore in der englischen Premier League erzielt. Beim Spiel am vergangenen Samstag gegen Newcastle United schoss er das erste Tor bereits in der 5. Minute, und seine Mannschaft siegte mit einem überragenden 5:1. Sein nächster Einsatz wird am 16. Februar in der UEFA Champions League gegen den französischen Fußballklub Saint-Germain sein.

Der FC Chelsea wurde 2003 von dem russischen Öl-Milliardär Roman Abramowitsch aufgekauft und ist eine von insgesamt nur vier Mannschaften, die bisher alle drei Europapokalwettbewerbe gewonnen haben. Seit Beginn der Spielsaison 2014/15 ist der 1,86 m große Costa beim FC Chelsea unter Vertrag.