After two holes, where he made a birdie-three and an eagle-three, it looked as if it was going to be Grace's tournament, but he double bogeyed the par-three sixth and bogeyed the par-four 12th to fall out of contention.
South Africa's JC Ritchie, who lipped out for an albatross on the 15th in a closing 65, finished two shots behind Grace in third.
The 29-year-old had started his round with a birdie and an eagle to briefly lead, and a four-under 68 completed a decent weekend.
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.
"I can't remember when, or if, I've ever made three eagles in a round but it was fun", he said.
"She doesn't play golf but she knows her way around a golf course".
A nerveless birdie putt on the 15th pretty much confirmed his champion status as he went five shots clear and set him on course for a maiden title on the European Tour. "Now I've played myself right back into it and I'm really excited going into tomorrow".
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The doctor was with me for most of that period and he chose to get us to the hospital and see what they could do about it. This is England's seventh successful chase of a 300-plus target, of which five have happened since the 2015 World Cup.
"At the moment it's weird, I feel like I didn't play incredible". "I certainly hope that I can keep that trend (of Englishmen winning the SA Open) going".
By the time he walked up the 18th fairway for the last time‚ Chris Paisley (and his wife and caddie Keri) followed in the footsteps of countryman Graeme Storm to clinch the title‚ and he too beat significant odds in the process.
Sharing fourth place at 14-under-par were Scott Vincent of Zimbabwe and the South African duo of Jacques Blaauw and Jacques Kruyswijk.
Grace, the highest ranked player in the field at number 30 in the world, also recorded three birdies and two bogeys as he attacked the pins, particularly on the front nine.
Koepka, the brother of PGA Tour campaigner and US Open champion Brooks Koepka, was delighted with his round after he opened with a bogey.
Retief Goosen and Charl Schwartzel head into the second round on three-under, while Ernie Els is at one-under.
But ex-US Masters champions Mike Weir (146) of Canada and Trevor Immelman (149) of South Africa bowed out after the second round.