Australian Herbert, who'd held an overnight two-shot lead after equalling the lowest round ever recorded at a men's major championship on Friday with his 62, was still setting the pace halfway through his third round on Saturday (Sunday AEST).
But it all began falling apart in the run-in after Herbert had bogeyed 15 and 16, and looked sure to drop another at the par-five 17th after he drove into thick rough, had to take a penalty drop and was left with a mercilessly tough blind three-iron to the green from a wispy lie on a dune from 244 yards.
He took a giant rip at the ball and, amazingly, it ended up finishing just 20ft from the pin.
"I think that's the best shot I've ever hit," Herbert confided to Sky TV course reporter, former Aussie pro Wayne Riley, who also hailed it as one of the best he'd ever witnessed.
"It was one of those shots you stood over, this is either going to be unbelievable or this could be the end of my tournament if I hit it straight into the bulrushes in front of me and run up some kind of double-digit score. I'm happy it came off. Yeah, I think that slots into the top-10 shots that I've hit."
Herbert ended up parring the hole, and though he hit another poor drive at the last and had to fire out of the rough to scrabble another battling par, the 30-year-old scraped together a one-over par 71 that still leaves him joint-fourth alongside American Ryan Gerard on seven under, three behind the soaring Burns.
Asked if he still felt he was in with a shot, the 30-year-old Bendigo star shrugged: "I think Sam Burns is going to be a man possessed. I think he's going to be very tough to beat. I'm not thrilled about giving him a three-shot head start, but we are where we are."
Burns shot a five-under 65 to lead by two shots from Korean Si Woo Kim and New Zealander Ryan Fox, who shot the third record-equalling 62 of the week following the landmark efforts of Herbert and Burns on Friday.
Fox had started in 52nd position but the son of New Zealand All Blacks' great Grant Fox ended up converting nine birdies to share the lead held overnight by Herbert, some 90 minutes before the Aussie even teed off.
It then proved a roller-coaster for the Aussie as conditions grew a little windier and trickier and he quickly squandered the lead, dropping a shot at the third, before rebounding with two birdies before the turn to regain the advantage from Burns.
The whole complexion of battle then changed in the denouement, with Burns, fresh from his US Open battle royal with champion Wyndham Clark, turning on the style as he birdied two more holes coming home.
"It's going to take some chasing down to catch Sam," said Herbert of the American who nearly decided to miss the final major of the season after his wife gave birth to their second child.
"But I've seen what I was able to produce over the last three days, and it's not something that's out of reach for me."
Burns thrived alongside Bryson DeChambeau, who was cheered by his army of fans following his two-stroke penalty over a rules breach on Friday and showed some resolve as he crafted a 69 to reach six-under, still in the hunt.
The top 20 are within six shots of each other. Among them is not just Herbert but his rather more unlikely Victorian pal, Cameron John, who shot 69 to finish four under, tied for 11th alongside a host of luminaries, including world No.1 Scottie Scheffler (70), who had more putting gremlins, Jon Rahm (70) and Xander Schauffele (66).
One shot better off at five under, despite cursing a disappointing finish, is local hero Tommy Fleetwood (69).
Adam Scott is tied-38th at one under after a 71, but Fox's amazing nine-birdie round showed what's still possible. It was climaxed by an incredible 183-yard strike from a fairway bunker at the last that helped him rescue par for the 62.
