World number 158 Gotterup carded nine birdies in a bogey-free 61 on Friday to finish the second round on 11 under par.
England's Harry Hall sits two strokes off the clubhouse lead after posting a six-under 64 to finish the day in second place.
The Australian challenge looks as if it will be once again be reliant on the veteran Adam Scott, but he's eight shots off the pace at three under for the tournament following his 68.
Elvis Smylie, the young Aussie who had enjoyed a good start with his opening 67, finished with a second-round 71 that leaves him a further shot behind, while Karl Vilips comfortably missed the cut with his 74 leaving him on five over.
Sheffield's Matt Fitzpatrick, the 2022 US Open champion, is joint third in the field alongside Marco Penge following respective rounds of 63 and 67, while Swede Ludvig Aberg, who made eight birdies before bogeying the last, shot 65.
McIlroy registered six birdies and one bogey on his way to a second-round 65 to leave him among a handful of players tied for sixth on seven under par.
A week before The Open at Royal Portrush, the Northern Irishman gained five shots in his first seven holes to build on a trio of birdies at the end of his opening round before momentum waned on the back nine.
"The conditions were so good for us this morning," said McIlroy. "It felt like if you didn't play that first nine in three or four under, you were losing strokes to the field.
"I did a lot of good things today, a couple of loose shots here and there but overall it was a good day. I'm excited for the weekend, right in contention."
Gotterup threatened to break 60 after sinking his ninth birdie of the day on the 14th hole but four pars followed.
"The 59 never really crossed my mind," said the 25-year-old.
"I made the putt on 14 and I was like, all right, I've got 16 and obviously 17 and 18 are pretty tough. So I really wanted to get 16.
"I'm not going to complain too much when I make my birdies on a course that isn't always typically easy."
US Open champion JJ Spaun missed the cut after three bogeys in a 72 left him two over, while world No.1 Scottie Scheffler is tied in 21st place after shooting a second round 68 to sit five under.
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