In a repeat of last season's FA Cup final, Chelsea took the lead through Willian towards the end of the first half before a brace either side of half time from Michy Batshuayi ensured a winning start for the Premier League champions.
It was Chelsea who started the match on top and they could have taken the lead inside three minutes when Cesc Fabregas threaded a pass through for Victor Moses, only for the wing-back to fire a tame effort straight at David Ospina in the Arsenal goal.
Ospina was beaten five minutes later when a mistake from Ashley Maitland-Niles allowed Willian to run through on goal, but the Brazilian rolled his finish past the far post with only the keeper to beat.
Batshuayi then tried his luck from outside the area on a couple of occasions in quick succession, but he didn't catch the shot as he would have liked and Ospina comfortably gathered both of his efforts.
Arsenal's first real sight of goal came midway through the first half when Mesut Ozil picked out Aaron Ramsey with a clever pass inside, but the Wales midfielder was at full stretch as he poked the ball wide of the target.
Chelsea were soon back on the front foot, though, and Willian was the next to come close with a low drive which was kept out by Ospina before Batshuayi saw a goal disallowed for offside from the resulting corner.
The first goal arrived moments later, though, as Batshuayi escaped his marker before playing a ball through for Willian, who cut inside past Nacho Monreal and curled a precise finish into the bottom corner off the inside of the post.
Having broken the deadlock Chelsea then made it two goals in as many minutes, with Batshuayi getting his own name on the scoresheet with another clinical strike, collecting the ball just outside the box before burying his finish into the bottom corner.
Arsenal's best chance of the first half arrived in stoppage time when Alex Oxlade-Chamberlain - who has been linked with a move to Chelsea this summer - found Ramsey inside the area and it took a smart save from Thibaut Courtois to deny the Arsenal man from a tight angle.
The Gunners made a host of changes at the interval, but it took Chelsea just four minutes of the second half to extend their lead when Fabregas and Marcos Alonso combined to tee up Batshuayi, who doubled his personal tally for the match with a stunning first-time strike into the top corner.
Arsenal did look more dangerous going forward in the second half, though, and Francis Coquelin rippled the roof of the net with a powerful drive that flew narrowly over before Ospina was called into action again to deny Willian.
Chelsea came close again with just over 15 minutes remaining when Fabregas's pass picked out the marauding run of Fikayo Tomori, whose first touch was perfect only for his eventual effort to be kept out by the keeper.
The game began to fizzle out with a string of substitutions from either side, but Arsenal did come close to a late consolation when Donyell Malen struck the outside of the post from a tight angle, although Chelsea keeper Willy Caballero looked to have it covered.
Chelsea held on to their three-goal advantage, though, and will now travel to Singapore to continue their pre-season schedule with matches against Bayern Munich and Inter Milan before meeting Arsenal again in the Community Shield on August 6.