The Gunners scored all three goals in a one-sided first half to earn a fourth league win in succession, lifting them up to third place in the Premier League table.
Chelsea, who have now taken just one point from the last nine on offer, were unable to cope with their rivals at times to make it back-to-back league defeats for Antonio Conte for the first time in seven years.
It was also a special occasion for Arsene Wenger in the week that marks 20 years as Arsenal manager, with the Frenchman avenging the 6-0 defeat suffered at the hands of the same opponents when celebrating his 1,000th game in charge two years ago.
The Blues' plan was clear to see from the off, as all 11 players got back behind the ball inside their own final third in an attempt to prevent their opponents' attacking players from finding a way through.
That tactic did not work, with Santi Cazorla given all the time in the world to fire away a shot five minutes in, before two quick-fire goals soon after put the hosts well in control.
While the inquest was still ongoing at the back, Arsenal pushed on and found a second when some quick-fire passing around the Chelsea box culminated in Nacho Monreal being slipped in down the right, before squaring for Theo Walcott to find the net on his 350th outing for the Gunners.
Chelsea saw weak attempts from Eden Hazard and Willian fail to trouble Petr Cech as the one-sided first half transpired, and the hosts were three to the good prior to the midway point after a two-on-two attack allowed Sanchez to return a pass to Mesut Ozil at the back post for the German to volley home a killer third.
The Gunners had failed to score in any of their last five meetings against Chelsea, while also failing to win any of the previous nine in the Premier League, but they had the points as good as secured by the halfway point in the game.
Conte waited 10 minutes into the second half until changing things around, bringing on Marcos Alonso for former Arsenal ace Cesc Fabregas - starting his first league game under the Italian - in a switch to a five-at-the-back system.
The chances dried up in a quieter second half at the Emirates Stadium, although Walcott did come close to bagging his second when slotted through, only for Courtois to produce a big stop down low.
It was to be a stress-free evening for Wenger on his special day, though, thanks to Chelsea's failure to register a single shot on target until the final throes of the match.
Substitute Michy Batshuayi was sent clean through on goal, yet he failed to get the better of Cech to make it a comfortable fourth league win in a row for Arsenal at the expense of their stumbling near neighbours.