Already with three European Tour titles to his name this season, the 24-year-old knocked two strokes off Lee Westwood's course record thanks to an eagle and 10 birdies - five of them in a row to finish with.
Fourteen players have now shot 60 on the circuit - Darren Clarke has done it twice - and like so many of the others Grace came off saying: "It could have been a 59".
The Pretoria golfer leads Victor Dubuisson by two, the Frenchman's 62 at St Andrews today also being a course record, while many of the big guns were left trailing in his wake after they battled with the far tougher Carnoustie.
The three Ryder Cup heroes in the field - Paul Lawrie, Martin Kaymer and Peter Hanson - returned 75, 70 and 72 respectively, with Lawrie commenting on his return to the course where he won the 1999 Open: "I was a little bit tired obviously, but the first 12 holes were my worst ball-striking of the year."
Current Open champion Ernie Els had to play the last eight in three under just for a 73, while Paul McGinley, favourite to take over from Jose Maria Olazabal as Europe's captain, struggled to a 76 and is down near the rear of the 168-strong field.
Highlight of the Irishman's day, in fact, was partnering Olympic and Paralympic runner Oscar Pretorius in the celebrity pro-am.
"It was a real honour to be in his company," he said.
When Westwood had his 62 at Kingsbarns in 2003 it included an albatross two on the ninth, but Grace needed nothing as extraordinary as that.
"I never really made anything long," he said. "It was all 12 to 15-footers and it's nice just to have a bogey-free round on a links.
"We were lucky with the weather, but you still have to get it in the right spots and get it around."
His eagle came on the 565-yard 16th, his seventh, and took him to five under, but it was on the outward half where he really went into overdrive.
Grace birdied all but the second and fourth and came to the 558-yard ninth needing an eagle for the 59, but pushed his second wide before pitching to a foot.
Amazingly, Dubuisson threatened to overshadow him at the Home of Golf when he reached 11 under with three to play.
Two more birdies and he would have had the elusive and magical 59, but the 22-year-old bogeyed the 371-yard seventh and parred the last two.
He switches to Carnoustie tomorrow, while Grace is at St Andrews.
Dane Thorbjorn Olesen is in third place after a 63 at St Andrews, while the best scores at Carnoustie were the 67s of England's Oliver Wilson and France's Gregory Havret.
Kaymer dropped his only shot of the day at the 18th - good job for Europe he did better than that at Medinah - while Hanson, far from happy about also playing only twice in America, recovered from three over to one under before also finishing with a five.
It was not only Lawrie returning to the scene of his Open triumph. So was Padraig Harrington, who won the Claret Jug in 2007 after a play-off with Sergio Garcia, and he signed for a 71.
Current Open champion Ernie Els was also at Carnoustie and said after his 73: "I was shocking on the front nine. I don't know where I was - Florida or somewhere."
He stood on the 11th tee four over, but birdied three of the next four holes and parred in.
McGinley was inevitably asked about the 2014 captaincy when he finished, but is not about to embark on any campaign for the job.
"As my caddie Jimmy says 'what's meant for you won't pass you by'," he commented. "I'll just have to wait and see".
The decision is expected to be taken by the players' committee in January. Darren Clarke, another of Olazabal's assistants, is also a contender, but world number one Rory McIlroy has already said he thinks his fellow Northern Irishman's popularity in the States makes him a perfect fit for the 2016 match in Minnesota.
Hanson stated: "I definitely see Paul (for 2014). I think he will make a great captain."