Grillo, ninth and 10th in this event in the last two years, carded a brilliant third round of 62 at East London Golf Club to lie 20 under par, two shots clear of England's Oliver Fisher.
The 21-year-old finished second in the Dubai Desert Classic at the start of the month, setting the clubhouse target thanks to an outrageous eagle on the 72nd hole when he holed from 60ft across the green after his approach had bounced back off the hospitality units behind the green.
Only birdies on the 16th and 17th from defending champion Stephen Gallacher denied Grillo a memorable victory, but the world number 149 has the chance to make amends after a brilliant display of putting on Saturday.
"I thought I had it for a moment (in Dubai) but Stephen played great on the last few holes so he got the trophy and I got second place, but it felt like a win for me. A great putt on the last hole gave me a lot of confidence for the rest of the year," Grillo told reporters.
Speaking about Saturday's round, he added: "It was a good round of golf, I played quite good but the putter helped the most. I made some good putts on the back nine to keep my round going. Like every round you miss a couple and of course I regret those, but it was a good score.
"I didn't hit it quite as close as I would have like for nine under, but the putter helped a lot. I made a couple on 12 and 13 from a good distance but I am quite happy with my game and hope to repeat it for tomorrow.
"You have so many scoring holes out here that when you start making a couple of pars in a row you start to be impatient so patience is the key out here and wait for the birdies. It was more difficult today than the past two days, the wind picked up but I played good enough not to care about the wind today."
American John Hahn had maintained his two-shot overnight lead for much of the third round until Grillo picked up his sixth and seventh birdies of the day on the 12th and 13th.
Hahn then fell out of a share of the lead with his first bogey for 47 holes on the 12th and Grillo pressed home his advantage with further birdies at the 15th and 16th.
That looked like securing a commanding lead until Fisher played his final four holes in four under par for the second day in succession, a two-putt birdie on the par-five 15th followed by an eagle from six feet on the short 16th after his drive took a fortunate bounce through a greenside bunker.
A birdie on the last looked unlikely when his approach came up short of the green, but the 2011 Czech Open winner holed a long-range putt to complete a second 66 of the week.
"You had to be aware of where you were placing your ball with this wind, but it was good fun out there," said Fisher, who lost his card at the end of last season but would secure an effective three-year exemption with victory on Sunday.
"I hit a few poor shots, but I'm delighted with the way I finished and pleased with my score for today. I'm two behind and it's the sort of course where guys can come from a long way back."
Fellow Englishman Richard Bland is two shots behind Fisher on 16 under after a superb 64, alongside home favourite Thomas Aiken and halfway leader Hahn, who struggled to a 71.