The Australian rising star began on top of the leaderboard at the Royal Queensland Golf Club in Brisbane, one clear of veteran Adam Scott (43), and never relinquished the advantage.
In overcast conditions, he had wobbles with bogeys at four and eight but kept his cool to be 17-under for the tournament as he edged closer to victory at the opening event of the DP World Tour's 2024 season.
Japan Tour stalwart Hoshino carded a 64 to be outright second, with his putter running hot on the back nine, where he rattled in six birdies.
Australian Curtis Luck, who nailed a hole-in-one on Friday, fired a bogey-free 66 to be a shot further back, one ahead of two-time tournament winner Scott, who is six behind Lee after an even-par 71.
"I played solid, I'm pretty happy with the way I went," said Lee, who is chasing a third win on the European circuit following victory at the 2020 Vic Open and the Scottish Open a year later.
"There was a little mishap in the middle, but I came back nicely. I've been hitting amazing shots and if I do have those blemishes, well, it's just golf."
Along with Hoshino, Scotland's Connor Syme was a big mover after six birdies in his opening nine holes. He signed off with a 64 that left him joint fifth alongside Australia's Lucas Herbert.
New Zealand's Michael Hendry also posted 64 to be to seven-under for the tournament.
Hendry was diagnosed with leukaemia earlier this year, forcing him to withdraw from the British Open to undergo bone marrow treatment, but is now in remission.
Lee, who won the Macau Open this year and has secured 2024 playing rights on the US PGA Tour, nailed two birdies in his first three holes and by the seventh had stretched his lead over Scott to four strokes.
A bogey at the eighth and birdies for Scott at nine and 10 reduced the deficit to one.
But that was as good as it got for the Australian veteran, who faded on the back nine.
"I couldn't really get it going and unfortunately I missed a putt on 12 and then bogeyed 14 and 16 and had a rough run coming in there," said Scott.
"So the momentum really changed and Min had a couple of birdies and we went from being quite close to I'm a long way back now."
