Diego Costa scored the winner after Per Mertesacker's early dismissal to give Chelsea a 1-0 victory over Arsenal on Sunday.
Mertesacker was shown a straight red after 18 minutes at the Emirates for bringing down Costa when he was in on goal.
Costa gave the visitors the lead five minutes later and Arsenal, who have now not beaten Chelsea in their last nine Premier League meetings, struggled to muster a response.
The home side managed just one shot on target as they failed to score against Chelsea for the sixth successive league match.
The defeat sees Arsenal remain third in the league, level on points with Manchester City and three behind leaders Leicester, who they face at the Emirates on February 14.
Chelsea, meanwhile, climb up to 13th and preserve their unbeaten record under Guus Hiddink after a hard-fought win.
Alexis Sanchez and Eden Hazard returned to the respective squads but only as subs, while Mesut Ozil and Costa were handed starting roles and Pedro missed out with illness.
Theo Walcott was named Arsenal captain, 10 years after joining the club, and the hosts spurned an early chance as Joel Campbell miscued a volley inside the box.
Former Chelsea keeper Petr Cech was then called into action to keep out a low shot from Oscar at his near post.
Chelsea looked the more composed side in an open start and Willian shot tamely at Cech after his volley rebounded back to him off Mertesacker.
The German was then involved in the most significant moment of the first half when he was shown a straight red for bringing down Costa, who looked to be in on goal after running onto Willian's through ball.
Gabriel, who saw red in the meeting earlier in the season, was sent on to fill the gap at the back in place of Olivier Giroud, who reacted with surprise before slowly trudging off.
The Frenchman barely had time to get the dugout before Chelsea took the lead, Costa getting ahead of Gabriel to turn in Branislav Ivanovic's cross.
With the numerical advantage, Chelsea dominated the remainder of the half, Costa slicing a back-post volley wide and then forcing Cech into a sharp save from a tight angle.
Ivanovic had a header cleared off the line in the 43rd minute while Arsenal's best opportunity came in injury-time as Mathieu Flamini flicked a volley over the bar after a clever through ball from Aaron Ramsey.
The visitors continued to control proceedings after the break but had appeals for a penalty waved away when Laurent Koscielny barged over Fabregas.
The introduction of Sanchez after 56 minutes gave Arsenal an extra spark and they soon went close to an equaliser as Hector Bellerin's shot was blocked after a goalmouth scramble.
But that was to be a rare opportunity for the Gunners as their attacking threat was largely nullified by Chelsea.
Thibaut Courtois almost handed the hosts a late chance when he fumbled a free-kick, but he was helped out by his defenders and Chelsea held on for victory.
Arsenal: Cech (6), Bellerin (6), Mertesacker (3), Koscielny (6), Monreal (5), Flamini (5), Ramsey (6), Campbell (5), Ozil (5), Walcott (5), Giroud (5).
Subs: Gabriel (6), Sanchez (6), Oxlade-Chamberlain (5).
Chelsea: Courtois (6), Ivanovic (7), Zouma (7), Terry (7), Azpilicueta (6), Mikel (7), Matic (6), Willian (7), Fabregas (7), Oscar (6), Diego Costa (7).
Subs: Remy (5), Hazard (5).
Man of the match: Cesc Fabregas