The home side needed less than a quarter of the game to open up a two-goal lead, with Pedro getting the ball rolling courtesy of a close-range finish after being teed up by matchwinner Alonso.
Jorginho played a key part in the opener thanks to his initial pass into Alonso's path from deep, and the Italian was one of a handful of Chelsea players being given freedom to pop up wherever they wanted.
The former Napoli man set a more advanced N'Golo Kante free soon after, but the Frenchman passed up the chance to shoot and instead laid it off for Ross Barkley, whose shot dripped onto the roof of the net.
Aubameyang was guilty of a huge miss moments later, skying the ball after being picked out right in front of goal by Hector Bellerin, and it would prove a big moment in the match as Morata cut inside Shkodran Mustafi and tucked past Petr Cech just 55 seconds later.
Despite being outplayed for large parts of the first half, the Gunners were still able to create further big opportunities.
Mkhitaryan somehow missed from a similar position to Aubameyang before him, but the Armenian made amends with his edge-of-the-box shot which crept out of Kepa's reach.
Four minutes later the visitors were back on level terms as, after Cech kept out Morata with a decent save, Iwobi was well positioned to convert Mkhitaryan's cutback from 10 yards.
Matteo Guendouzi was next to get a shot on target in an action-packed first half, while Iwobi and Aubameyang should have done better with their efforts from inside the area.
The first chance of a quieter second period fell to Kante, who could only fire the ball at Sokratis Papastathopoulos, while Barkley's low shot was pushed aside by a busy Cech.
Chelsea were the side enjoying more of the ball in dangerous areas of the field as the game entered its final half-hour, boosted by the introduction of Hazard and Mateo Kovacic from the bench.
Jorginho tested Cech with a deflected effort and David Luiz had a dipping free kick kept out by the former Chelsea stopper as the Blues went all out in search of a winner.
Sarri's men were rewarded for their perseverance late on when Hazard created some space for himself down the left and squared the ball to Alonso for a simple finish.
Former Arsenal striker Olivier Giroud and current Gunners ace Aaron Ramsey were both unlucky with their shots in the dying embers of the game, with Chelsea seeing things through for three vital points.
CHELSEA (4-3-3): Kepa; Azpilicueta, Rudiger, David Luiz, Alonso; Kante, Jorginho, Barkley (Kovacic 60'); Willian (Hazard 61'), Morata (Giroud 75'), Pedro
ARSENAL (4-2-3-1) Cech; Bellerin, Sokratis, Mustafi, Monreal; Xhaka (Torreira 46'), Guendouzi; Mkhitaryan, Ozil (Ramsey 68'), Iwobi (Lacazette 75'); Aubameyang