Lee, who prevailed in his duel with Hoshino last week in to win the Australian PGA Championship, needed a 10-foot birdie putt at the last to complete a scrappy round of one-under-par 70 and get back on terms with his Japanese rival on 13-under.
Hoshino had jumped into the leading pack at the 14th when he hit an iron shot to within two metres of the pin and sank the eagle putt, before taking the outright lead by draining a birdie putt at the 18th for a six-under-par 65.
Briton Alex Fitzpatrick, who shot a fine 66, and American Patrick Rodgers, who signed for a 68, are still very much in the hunt for the Stonehaven Cup in a share of third on 12-under.
Lee threatened to make the tournament a procession when he birdied the first to extend his overnight lead to four strokes but a double bogey at the third, when he went from trees to water, dragged him back into the chasing pack.
"It was a bit of a grind," the 25-year-old told reporters.
"It wasn't the easiest of rounds like the last five I've played. But golf is golf. I felt like I got a little unlucky with some lip-outs towards the end, but it is what it is.
"I played great (in the final round) last week, so hopefully I can finish it off tomorrow."
Former US Masters champion Adam Scott (67) remains just about in the hunt for a second Australian Open title five shots behind the leaders, while Cameron Smith, the 2022 British Open winner, was a further two shots back after a 69.
The novel format of the Australian Open has men and women competing for their respective titles on the same course at The Australian Golf Club.
A hot start allowed reigning women's champion Ashleigh Buhai to quickly haul in South Korean overnight leader Shin Ji-yai, who suffered from a cold putter during her round of par 72.
South African Buhai holed out from the bunker at the fourth to complete a four-birdie start to her round of 67 and will take a three-stroke lead over former world number one Shin into the final round.
"There was a bit of excitement after holing that bunker shot, but then I did really well to calm myself down and just stay in my moment and just concentrate on what I’m doing," said Buhai, who finished on 12-under for the tournament.
Lee's older sister, double major winner Minjee, stands alone in third place on five-under after also shooting a 67.
