The Zambian was in a share of the lead as he stood on the 13th tee of the Firethorn Course at Randpark Golf Club but he missed the green with his second and three-putted to slip back into the pack.
He responded brilliantly with birdies on the 14th and 15th, and a 12-footer on the 16th had him in the solo lead at 11 under before Charl Schwartzel edged ahead of him with a brilliant 63.
“I was pleased that I managed to bounce back after the blemish,” he said. “I am very happy that I was able to hang in there and not let that distract me in terms of finishing off the round.
“I am pleased with where I am. I think I have taken the right steps to play good golf and the next thing for me is to play good golf again. I think everything else will just take care of itself.”
Home favourite Louis Oosthuizen was pleased with his own battling qualities as he ground out a 70 to sit a shot behind Muthiya.
The 2010 Open Champion bogeyed the first but broke a run of ten pars with a hat-trick of birdies before dropping a second shot of the day on the 16th.
"I felt I just kept it together and just got the round done and didn't play myself out of it completely,” he said. “It was just a day like that where you couldn’t really get cross, you just need to get through the round and stay patient.”
Kurt Kitayama was pleased with his mental strength as he follows up his win in Mauritius last week, and he will also head into the weekend two shots behind Schwartzel.
“I was able to grind out a couple under, stay in it and get into the weekend, that’s where I want to be,” he said.
“It’s a great position to be in but I still have 36 more holes to play, right now I’m just trying not to think about it too much.
“It’s been a great two weeks and hopefully we can just keep it going. For the weekend, I will just look at where the pins are when the pin sheets are sent out but other than that, I’ll just try to keep my mind off golf.”
Zander Lombard finished top of the leaderboard at the Qualifying School in November to regain his playing privileges and had to battle adversity again on Friday.
After a birdie on the first, the South African went bogey, triple-bogey but recovered for a 68 to sit alongside Oosthuizen and Kitayama at ten under.
“I think the biggest thing is that old cliché of sticking to your process and doing your thing,” he said.
“You can’t control the past and you can’t control the future so you’ve just got to stay in the present, stick with your game plan and luckily it worked out after that, so I’m happy with the round.
“Life’s better than it was two months ago, I can tell you that. I just proved to myself that I belong here and it’s nice to be in contention in South Africa and showcase what I can do.”