Otto had seven birdies and an eagle, leaving him at 14 under on Jack Nicklaus-designed the Serengeti course.
Otto is bidding for his second European Tour title and first since the 2008 Italian Open.
"I haven't won it yet," he said. "It's a new day tomorrow."
Otto has appeared calmer on the course of late after once throwing his clubs into a river during a tournament on the local Sunshine Tour.
"I'm not a guy who gets all nervous," he said. "Maybe angry, not nervous."
Goosen, two-time South African Open winner, shot a 71 in a round marked by birdies on the first three holes and bogeys at Nos. 9, 13, 17 and 18.
Els, who last year won the national open for the fifth time, soared to a 76 and is tied for 53rd. He took a nine on the par-5 No. 16 after hitting his tee shot into the water. He was on the green in six and three-putted.
Els was twice forced to step away from his tee shot because of fans taking photos on their cell phones while he was lining up.
"They should ban the guys and get them to hand in their cell phones," said Otto, his playing partner. "It gets to you."
Carlsson carded a 66 to put him at 11 under. He was the lone player not from South Africa among the top seven. He needs a top-two finish to keep his tour card for 2012.
"I'm not going to think about it," Carlsson said. "I'm not going to make stupid decisions."
Mulroy, who won the Alfred Dunhill Championship last week for his first European Tour title, shot a 68. He recovered from four bogeys in his front nine to make four of his six birdies on the way home.
Second-round leader Steven O'Hara of Scotland shot a 74 and was among those five shots off the lead.