The west London side were handed a boost when Per Mertesacker received a red card for hauling down Diego Costa in the 18th minute at The Emirates.
The controversial Chelsea striker punished the Gunners minutes later after he guided a close-range finish past former team-mate Petr Cech.
Belgium international Courtois was understandably delighted with Chelsea’s second Premier League win under new manager Guus Hiddink.
Courtois wrote on his Instagram page: “Big win today! Great effort from everybody! Fantastic support from our fans! #CFC”
Chelsea haven’t lost to Arsenal in the Premier League since a 5-3 defeat at Stamford Bridge in 2011.
The defending Premier League champions are in 13th place and seven points above the relegation zone.
The Blues are still 14 points behind fourth-placed Tottenham Hotspur in the race to secure a place in next season’s Champions League.
Hiddink’s side make the trip to Watford in their next Premier League game on Wednesday 3 February.
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