Per Mertesacker's 18th minute dismissal for pulling down goalward bound Diego Costa proved the turning point in Sunday's match at the Emirates.
Soon afterwards, Costa scored the only goal of the match after volleying home an excellent cross from Branislav Ivanovic.
In a game of few chances, Chelsea was content to maintain its lead in a solid defensive display, Arsenal restricted to a first half chance for Mathieu Flamini, set up by Aaron Ramsey.
The same two players also had a glimpse of goal in a scramble in the Chelsea penalty area in the second half.
The only cheering note for the Gunners was the introduction of Alexis Sanchez as a substitute after a long injury layoff for the Chilean star.
But the 1-0 defeat left Arsenal in third place, three points adrift of surprise leader Leicester and behind Manchester City on goal difference.
Its north London rival Tottenham Hotspur is in the final Champions League place -- two points further back -- after a Dele Alli wonder goal in a 3-1 win at Crystal Palace Saturday.
Chelsea moves up
Chelsea is up to 13th, but fully 14 points adrift of a Champions League spot after a disastrous early campaign under Mourinho, to be replaced by interim manager Guus Hiddink.
The Dutchman secured a victory over Arsenal in his previous spell in charge of Chelsea in 2009 and was repeating the feat again, his side looking the sharper even before German international Mertesacker saw red.
Arsenal manager Arsene Wenger was left frustrated by the sending off, which he said was "harsh" but heartened by the return of talisman Sanchez with his team still challenging on three fronts.
Sunday's early kickoff in England saw Swansea ease its relegation problems with a 2-1 away win at Everton in the first match in charge for Italian coach Francesco Guidolin.
Visitor Swansea went ahead though Gylfi Sigurdsson's 17th-minute penalty but Everton was level nine minutes later when Gareth Barry's clever near-post flick was turned into his own net by the Swans' Jack Cork.
But Swansea regained the lead in the 34th minute when Andre Ayew's shot deflected in off the sliding John Stones.
Swansea climbs to 15th spot but more importantly four points clear of the drop zone.
Madrid sides held
In Spain, like Arsenal, Atletico Madrid fluffed the chance to regain top spot when held goalless by Sevilla, despite the visitor playing for 30 minutes with 10 men after Vitolo was sent off for a second yellow.
Later city neighbor Real Madird was held 1-1 in Seville by Real Betis, the first points dropped since Zinedine Zidane took charge.
A win would have taken Diego Simeone's Atletico team two points clear of Barcelona, which has played a game less, the top two playing in a key clash in the Nou Camp next weekend.
Atletico star striker Antoine Griezmann had its best effort in the second half, heading against a post, but Sevilla proved resolute.
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