Coetzee, 31, first played the Pretoria Country Club layout in an upscale suburb when he was 10 and won the Tshwane Open there three years ago.
Starting his round at the 10th, he staged a birdie blitz on his first nine, securing six within seven holes from the 12th, and added one more later.
Chilean Felipe Aguilar and Finn Mikko Korhonen, a Tshwane Open runner-up last year, share second place one stroke behind Coetzee.
Aguilar shot a 67 that included an eagle in hot, clear conditions while Korhonen matched Coetzee with a birdie-peppered 64.
Overnight leader Louis de Jager managed only a par 71 and shares fourth place with fellow South Africans JC Ritchie (67) and Justin Walters (68) and Portuguese Ricardo Gouveia (68).
“I am happy to have posted two pretty good rounds,” three-time European Tour winner Coetzee said.
“I will try and just focus on playing decent golf and posting good scores during the final two rounds at the weekend.
“It was a nice stretch on the back nine — my front nine — where I got a lot of birdies in a row.
“On the front nine — my back nine — I felt like I played pretty well, I just did not get the ball in the hole. I guess that is the way golf works.
“My short game feels good and it keeps me in the mix.”
Coetzee will hope to become the fifth South African winner of the six-year Tshwane Open with Ross Fisher of England to only foreigner to finish first.
Korhonen had an eagle and six birdies on a card spoilt only by a bogey five on the first hole of the 6,476-metre/7,081-yard course.
Two-time European Tour winner Aguilar sparkled on the first nine with an eagle and three birdies, but a less impressive second nine produced only one birdie and two bogeys.
American Julian Suri, ranked 70 in the world and the only top-100 golfer in the field, slumped to a 74 after sharing second place overnight and is eight shots off the pace.
His front nine included two birdies, two bogeys and two double bogeys and the second nine of an erratic round had three birdies and two bogeys.
Former US Masters champion Danny Willett of England, the only Major winner in the tournament, shot a 68 and is seven strokes adrift of Coetzee.