Danny Willett withdrew for the third time in his last five events as he elected to cut short his time at the Dubai Duty Free Irish Open.
Im's final-hole bogey saw him slip him in to a four-way four for fourth and miss out on Open qualification due to his lower world ranking than Fox, who joined Drysdale and Justin Rose eight strokes back.
"It was going OK through the seventh hole but things started to wobble from my second shot on the eighth", said Matsuyama, who made his first bogey of the day at the par-4 eighth. He moved three ahead with another gain at the par-5 7th and the advantage was extended to five after further birdies on the 8th and 9th holes.
Coming off a career-best 63 on Friday, the 35-year-old Australian reached 20-under 196 in the first year event at Thornberry Creek - the Oneida Nation-owned resort near Green Bay. "To keep up with the leaders I have to play explosive golf on the last day", he said. "It's such a great country, such a great history in the tournament, such a great golf course and, to me, such a great week".
England's Matthew Southgate finished second alongside Scot Richie Ramsay, who secured himself a place at the Open Championship in the process. Daniel Im of the United States and Spain's Jon Rahm share the lead at 17-under.
Jon Rahm moved into a share of the lead in only his second regular European Tour event as birdies continued to flow at the Irish Open on Saturday. "But if you had told me I was going to shoot 24 under in this weather, and win by six, I would have probably said, 'You're insane".
World No. 11 Rahm, one of the hottest golfers this season, could match the feats of Ballesteros, Jose Maria Olazabal and current Masters champion Sergio Garcia by winning the Irish Open.