In front of a packed house of 45,000 fans at the Toyota Stadium, the Gunners got off to a superb start as Olivier Giroud opened the scoring early on.
Miyaichi put away a penalty midway through the first half, and Theo Walcott netted on 55 minutes to extend the visitors' lead.
J.League outfit Grampus did pull a goal back through Kisho Yano but Arsenal ran out comfortable winners.
They took their goal tally to 17 in pre-season friendlies, with six of those scored by Giroud. Tomas Rosicky was the provider on this occasion, delivering an accurate cross from the right flank after just three minutes which the France striker nodded home with ease.
Arsene Wenger was again fielding Bacary Sagna as a centre-back alongside Per Mertesacker but the defence was not seriously tested by Grampus.
The crowd were particularly enthusiastic whenever returning hero Miyaichi, who grew up in the area, received the ball for Arsenal - and it was the Japan international who was next to get on the scoresheet.
A quick break involving Walcott and Giroud down the right ended in Tulio Tanaka handballing inside the box on 26 minutes. Miyiachi's powerful penalty was struck to the right of Seigo Narazaki to double the visitors' lead.
In the second half, 16-year-old midfielder Gedion Zelalem was one of four substitutions made by Wenger and he claimed an assist when playing an excellent pass through the defence for Walcott to coolly dink home on 55 minutes.
Grampus claimed a goal back in the 72nd minute when a cross from the right was headed in by former Japan winger Kisho Yano.
Arsenal are back in action on Friday when they take on Urawa Red Diamonds at the Saitama Stadium (kick-off 11.30am BST).