Jamieson, whose sole DP World Tour title to date came in the Nelson Mandela Championship a decade ago, carded nine birdies in a bogey-free second round of 63 to reach 13 under par and set a new course record.
England's Nathan Kimsey, who won the Challenge Tour Grand Final a month ago, carded two eagles and five birdies before dropping his only shot of the day on the 18th after firing his approach over the green into the water.
Compatriot Eddie Pepperell was also on 10 under after making six birdies on the back nine in his 65, with France's David Ravetto on the same mark thanks to a second consecutive 67.
Pepperell told Sky Sports: "After a few holes I wasn't sure what to expect with the weather and how the course might play. It was a tough start and then the weather passed and it was quite calm and scoreable.
"I didn't feel terribly comfortable off the tee for the second half of the round, but I hit my irons very well so it was just a case of getting it in play and I felt like I was going to flag hunt most of the way in, which I did, and holed a few putts."
South Africa's Dylan Frittelli shot a second round of 66 to sit in 10th place on eight under par, having somewhat unusually had to enter Tuesday qualifying.
Frittelli told Sky Sports: "I was pretty happy with six under par today. I made a few mistakes, but all in all a pretty good round.
"I've lost my status in Europe, don't play there any more, and Sunshine Tour winner's category had run out after winning five years ago, so I'm at the back of the field when it comes to getting in tournaments and didn't get an invite so decided to go to qualifying and shot 67 at ERPM (Golf Club in Boksburg, a 4.5 hour drive away from Leopard Creek).
"Here I am in the tournament competing for the lead, so definitely made it worth it going to qualifying."