Inclement weather forced the suspension of Friday's second round, meaning 61 players had to return to the course Saturday to complete their second 18 holes.
As a result, Clarke and Immelman were only able to complete four holes of their third rounds.
Both players picked up a couple of shots to get to 11-under. They jumped over second-round leader Bruce Vaughn. The American ended round two at 10-under, but dropped a stroke over the first four holes of his third round.
Fellow American Scott Dunlap is three back. He is also through four holes of round three.
Tournament officials have admitted another delay will force the event to be reduced to 54 holes. Even if the bad weather holds off, it may be pushed back to a Monday finish.
Vaughn made four birdies and an eagle to conclude his second-round 6-under 66 to take the outright lead. Clarke had a 72, while Immelman shot 68 to get to 9-under.
It was a remarkable performance considering Vaughn collapsed three times during his round because of a botched knee operation that has almost crippled him.
Late last year, Vaughan went in for a routine operation to repair a meniscus tear in his left knee that should have taken only 25 minutes. Instead, it took two operations by two separate surgeons.
After the first operation was botched, the second surgeon told Vaughn, 'I advise you to find an attorney.'
The first guy just flat butchered it. Simple as that, Vaughan said. Its a nothing operation. Ive had it done on the right knee and know guys that have had four or five of them done to the same knee. I cant recover from it. The guy killed the cartilage, so Im going to have to have a partial knee put in.
I went to see a doctor in Johannesburg and hes one of the best in the world. Hell work on it and says Ill get about seven years out of it and then have to have a total knee done.
Its just stupid. Im 46 years old. I ve seen a podiatrist here and hes got me some wedges for my shoes to help push the knee in the right direction. But I still went down three times in the round. It gets a sharp pain and locks up.
Vaughan said the severity of the pain brought him to the point where he could understand why people commit suicide.
I was going crazy sitting at home. Its been bad. I know how somebody could commit suicide. Ive been in that much pain, 24 hours. Id sleep about two or three hours a night. I never touched a club for two months until I came to Cape Town (for the South African Airways Open).
I knew the physios would do something over here. When they saw it (the knee) the first day in Cape Town, they couldnt believe it.