Murless, a co-leader after the first round, finished birdie-eagle on the East Course at Royal Johannesburg & Kensington Golf Club to move one shot ahead at 9-under 133.
Spain's Pablo Larrazabal was alone in second place at 8-under 134 following a 68 Friday, also on the East Course.
Warren Abery (65) and Charl Coetzee (67) went low at the West Course to get to 7-under 135, where they were joined by fellow South African Tyrone Ferreira, who had a 70 on the East Course.
Magnus A. Carlsson (66), Paul Waring (67), Iain Pyman (68), Joakim Backstrom (68) and Alex Haindl (68) were tied for sixth place at 6-under 136.
Murless was one shot off the clubhouse lead after 16 holes before closing with consecutive 3s for his 68.
After making birdie from the rough at the short 17th, Murless hit a soft 3-wood into the green at the par-5 18th and was left with a 5-foot putt for eagle, which he made.
It gave him his first overnight lead on the European Tour.
'I just trusted it and put the best swing I could on the shot and it worked out beautifully,' Murless said of his three-wood at the 18th.
Recalling a similar putt he missed on the same green last year, Murless readjusted for a bigger right-to-left break this time and rolled it into the cup.
'[L]ast year I misread it and under-putted. Cost me a couple of bucks, so I guess I learned my lesson,' he said.
Murless, a Johannesburg local, said he's been playing the RJ&K East Course since he was about 12 years old. Which gave him an advantage over most of the field as the first two rounds were plagued by rainy weather and wet conditions.
The second round was delayed an hour because of the weather, and standing water on the courses slowed play considerably. Showers were forecast for the weekend.
'If you can just hit the fairways, hit the greens and keep it in play, you can score here,' said Murless. 'Try to keep it simple and play this golf course the way it was designed to be played and hopefully everything stands up.'
Larrazabal stood at 7-under par with six holes to play when Murless finished his round and made it into the clubhouse. But he managed just five pars and a birdie to end a stroke back of the leader.
Andre Cruse (68), Louis Moolman (69) and Gary Boyd (69) were tied for 11th place at 5-under 137, while Darren Clarke (65) led a group of six players who were another shot further back at 138.
The cut line fell at even-par 142 with 80 players in a large field of more than 200 making the weekend.
This event is co-sanctioned by the European Tour and South Africa's Sunshine Tour.