There was a loud sigh from a huge crowd gathered round the final green in Vilamoura as the Glaswegian's chip shot for birdie from rough behind the flagstick hit the hole and stopped four inches from dropping.
Jamieson's score of 11-under- par 60 - an Oceanico Victoria course low - for a 14-under par tally leaves him in a four-way share of second place as he bids to claim his second Tour victory of the season this afternoon.
England's Paul Waring, seeking a first win in 118 events, led by two ahead of the final round after birdies at his 16th and 17th holes gave him a 67 for a 16-under total of 197.
Jamieson, who made the halfway cut with only a shot to spare, rocketed up the leaderboard from a share of 52nd after an effort that included 11 birdies and four in succession from the fourth hole.
"I was right in the zone and I've never ever felt that way before on a golf course," the 29-year-old said. "It was a 10 out of 10 round where I couldn't do anything wrong.
"I said to Richard [his caddie] while playing 17, 'I really want to make a birdie here so we have a chance of [a 59] going down the last and I could not have asked to hit a better shot in. It pitched just short of the hole.
"When I birdied the 13th I said to Richard, 'a few more and we could be part of history'. I was definitely nervous but thinking about it from the tournament point of view the leaders were going to be a minimum of 16 under going into the final round so that kept pushing me on."
Jamieson, only the 17th player in the 41-year history of the Tour to post a round of 60, had started the event with a 66 but followed that up with a disappointing 73.
"I played really well the first day and got nothing out of it. I was five under par but the longest putt I holed was maybe eight feet for par on one hole," added the Nelson Mandela Championship winner.
"I played the last four holes on Friday really well but found a swing key involving my right knee and keeping it a bit more solid so much so that I didn't need to go to the range and that really worked today. I feel like I have been playing well for a while. Yesterday I didn't necessarily play poorly, just didn't score well so it was nice today."
Jamieson shot 57 on his way to winning his first European Tour title in a play-off at the South African event last December, but that was in a tournament cut to 36 holes and on a Royal Durban course reduced to a par-65 because of saturated fairways.
Fellow Scot Chris Doak, despite a closing hole bogey, kept alive his hopes of a victory that would secure his Tour card for next season by shooting 69 for a share of sixth place on 13-under par.
"It was disappointing to end with a bogey because I thought I had hit the 5-iron well and it just ballooned in the air and hit the rocks but luckily didn't go in the water," Doak said.
"That was my first bogey in three rounds so while it would have been nice to stay bogey free, overall I can't complain. With one round to play my thoughts will be the same as they've been all week - just to try to stay calm and relaxed and enjoy the golf and see what happens."
Doak arrived on the Algarve lying 112th on the Race to Dubai money list and two places away from holding on to his Tour card.
He is due to head to Australia tonight to compete in the final regular event this year, the Perth International. But another good round today would see him retain his card and he could be tearing up his airline ticket and seeking a visa for China for the BMW Masters which starts in Shanghai on October 24, the first of the four lucrative final series events.
Meanwhile, Bathgate's Stephen Gallacher played his last dozen holes in six under par yesterday en route to a 65 and share of 11th place on 11-under 202. David Drysdale (69), Paul Lawrie (73) are on 208 with Richie Ramsay (70) two shots further back.
Waring, playing on a medical exemption this season after an operation on a serious wrist injury, looked to be drifting out of contention when he bogeyed the par-5 fifth and fired his approach to the ninth over the green.
But the 28-year-old from Birken-head chipped in for an unlikely birdie and collected four more on the back nine to move two shots clear of Jamieson, playing partner Hennie Otto, Ireland's Simon Thornton and Jamie Donaldson of Wales. "It was very good towards the end of the round," said Waring, who had the first top-five finish of his European Tour career at the Spanish Open in April and has had three more top-10s since.