The South African shot a six-under 66 to total 14-under for the tournament ahead of the final round at Glendower Golf Club.
After four front-nine birdies, he picked up three more during the inward trek but also bogeyed a couple of holes.
"I'm going to try and run with the momentum from the Nedbank Golf Challenge, be more patient, get things happening and not force anything", Grace said. My putting stroke was maybe a bit quick and I was pushing or pulling the ball.
Johnson and Kirk kept clean cards playing on opposite sides of the draw and closed with different brands of birdies on the par-5 18th hole - Kirk two-putted from about 10 feet, while Johnson found a bunker, laid up and hit a wedge to 5 feet.
Chasing Paisley and Grace on Sunday will be a three-man group at 12-under-par, three off the pace.
"Zack told me the whole day, 'You know, you're hitting it well".
Early in his third round it appeared Grace would not be among the contenders as he went to the turn just 1-under for the day and six off the pace being set by Paisley. But in the final round I just want to make sure I don't get in my own way, just take it shot for shot and stay in the moment.
English duo Andy Sullivan and Matt Wallace carded three-under 69s to move to five under for the championship while former Ryder Cup victor Jamie Donaldson, who carded the first ace of 2018, is a further two shots back after a one-under 71 which saw the Welshman mix five birdies with four bogeys.
Despite the frustration he felt through those holes on the front, Grace was always positive about his chances of a good finish. "Now I've played myself right back into it and I'm really excited going into the final round".
Paisley, on the other hand, had a quiet and steady afternoon in which he made a single bogey and three birdies to get to 15-under.
"Being tied for the lead isn't a position I've been in a lot", Paisley said.
"At the moment it's weird, I feel like I didn't play unbelievable". "I drove the ball really well and I felt like I actually played better than yesterday - just didn't really hole the putts".
That group contains overnight leaders Branden Grace and Chase Koepka, Zimbabwe's Scott Vincent, and Retief Goosen, the two-time U.S. Open champion who hasn't won a professional tournament since 2009.
Another home player, Darren Fichardt, sits in sixth on -11 after a 64 while compatriots Jacques Kruyswijk and Trevor Fisher Junior have joined Denmark's Jeff Winther on -10.