The pair is knotted at 11-under-par 205 and is two clear of Jarrod Lyle at the Daniel Island Club.
Lyle, an Australian like Sim, carded a 4-under 68 on Saturday and is alone at 9-under-par 207. Brendon de Jonge and Craig Lile both shot 70s in round three and are tied for fourth place at minus-7.
The second round was completed on Saturday morning as the tournament finally caught up after a weather delay during Thursday's opening round.
Sim took the lead from Stadler on Saturday morning, but really never got going in the third round. He bogeyed the second hole, then collected his first birdie at the par-5 sixth.
The Australian bogeyed the par-5 11th to fall all the way down to 7 under par for the championship. He needed a late rally to catch up to Stadler and that's exactly what Sim got.
He birdied four in a row from the 14th, but could not get down for birdie on the par-5 closing hole and nearly found the water with his second before settling for par.
'I was just hitting quality golf shots and managed to sink a few putts,' said Sim, who missed almost two months this season due to a back injury. 'It's just nice to be playing again.'
Stadler, who could collect his third win of the year and can earn a 'battlefield promotion' to the PGA TOUR, played much better than his fellow co-leader over the first nine.
He birdied three in a row from the sixth to reach 10 under par for the tournament. Stadler got to minus-12 thanks to birdies at the par-5 11th and the par-4 14th.
Things went downhill for Stadler after the birdie at 14. He dropped shots at both 16, thanks to a poor drive, and at 17 when he three-putted to fall out of the lead.
He joined Sim thanks to a birdie at the 18th.
'I felt pretty controlled all day,' acknowledged Stadler. 'I didn't hit it quite as crisp today, but still hit it pretty good. I feel like I'm hitting it pretty well.'
Gavin Coles (69), Peter Tomasulo (70), Chris Tidland (70), Tom Johnson (70), Chad Collins (70) and Craig Bowden (72) are knotted in sixth place at 6-under-par 210.