Gotterup, the world number 158, followed his course record-equalling 61 with a level-par 70.
And Clark matched McIlroy’s 66 welcome to provide welcome relief amid his torrid season.
The 2023 US Open winner has missed the cut in two of his past three events and mustered just one top-10 finish this year.
“It’s just nice to be back in this position and let’s see if I can go put a good round together and have four solid days of golf,” said Clark.
“I’ve hit a lot of good putts all year and just haven’t holed anything. Now it’s nice to see the ball go in the hole. Made a couple adjustments and they seem to work.”
Ludvig Aberg was jostling for the lead before a triple-bogey seven on the 13th was sandwiched by bogeys as he spilled five shots in a wretched three-hole stretch.
The Swede’s 71 leaves him four shots back.
World number one Scottie Scheffler is one further adrift after a frustrating 71 in which he had to wait until the 13th for a first birdie.
Frenchman Romain Langasque provided a wonderful moment with a hole in one on the 145-yard par-three 14th.
Having scraped into the weekend, defending champion Bob MacIntyre is one over after labouring to a 72.
