Following a goalless first half in Azerbaijan, the all-English affair burst into life after the restart with five goals being scored.
Olivier Giroud opened the scoring against his former side with a swooping header, Pedro added a second and Eden Hazard made it 3-0 from the penalty spot in a calamitous opening 20 minutes to the second half for Arsenal.
The Gunners were given some temporary hope when Alex Iwobi scored a sublime goal two minutes after coming off the bench, but Hazard doubled his tally for the evening to sign off in style in what was billed as being his final game in a Chelsea shirt - something he all but confirmed in the post-match celebrations.
Victory for Chelsea gives Maurizio Sarri silverware in his first season at the club to go with a third-placed finish in the Premier League, while Arsenal will now have to compete in this competition again next term as their route into the Champions League was blocked by their city rivals.
Chelsea were handed a major boost ahead of the match as N'Golo Kante, rated as 50-50 by Sarri on the eve of the game, was passed fit to play.
The big team news as far as Arsenal were concerned, meanwhile, was the inclusion of Petr Cech in goal against his former side in what was his final match before retiring in the summer.
Some 2,500 miles from home, it was the Gunners who started the better of the London rivals as Pierre-Emerick Aubameyang blazed wide from a good position and Alexandre Lacazette had a strong penalty shout rejected.
Chelsea ended the first half on top, however, with Emerson Palmieri and Giroud both testing Cech - the latter nearly picking out the far corner from the edge of the box, only for Cech to produce the first of a number of fine saves.
The Blues were also goalless at half time when they won this competition against Benfica in their only previous participation in 2013, and they did not have to wait long into the second half before opening the scoring.
Emerson sent in a flat cross, which Giroud did well to stoop down and guide away from Cech into the bottom corner after getting in front of a static Laurent Koscielny.
Chelsea's second was provided by Pedro, who sent the ball spinning away from Cech after being teed up by Hazard in the box.
Sarri's men had some breathing space five minutes later when Ainsley Maitland-Niles barged into Giroud inside the area, gifting Hazard the chance to convert the penalty down the middle.
Iwobi sent a half-volley flying past Kepa to give Arsenal a lifeline, but three minutes later Hazard tucked the ball home with a composed finish after exchanging passes with Giroud to kill off the contest for good.
The game became very stretched as Aubameyang had a shot saved off the line by Andreas Christensen following Kepa's save from Lacazette, but Chelsea cruised over the line to add another major honour to their collection.
CHELSEA (4-3-3): Kepa; Azpilicueta, Christensen, Luiz, Emerson; Kante, Jorginho, Kovacic (Barkley 76'); Pedro (Willian 71'), Giroud, Hazard (Zappacosta 89')
ARSENAL (3-4-1-2): Cech; Sokratis, Koscielny, Monreal (Iwobi 66'); Maitland-Niles, Torreira (Guendouzi 66'), Xhaka, Kolasinac; Ozil (Willock 77'); Lacazette, Aubameyangbody check tags ::