The 26-year-old posted an eight-under 134 total, one stroke better than Japan's Yuki Inamori (68) after 36 holes of the Japan Golf Tour event.
Koepka (68) trod water for much of the day, before vaulting within three shots of the lead thanks to consecutive birdies on the final three holes.
First round leader Koumei Oda, however, had a day to forget as he plunged five shots behind after a 73.
Leader Grillo, the world number 48, has been in good form recently, tying for second at the PGA Tour CIMB Classic in Kuala Lumpur last month, before tying for 14th at the WGC-HSBC Champions event in Shanghai two weeks later.
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Koepka, meanwhile, was going the wrong way after a bogey at the 12th, a lapse he attempted to rectify with an aggressive play on the short par-four 13th, where he tried to drive the green.
His tee shot, however, clattered around in the trees guarding the dog-leg, before nestling in a precarious spot on pine needles adjacent to the green.
He somehow threaded his recovery pitch shot through the trees to the edge of the green and proceeded to save par, but bogeyed the next hole before fighting back with the hat-trick of late birdies.
(Reporting by Andrew Both in Tokyo; Editing by John O'Brien)
