The pair were tied at 15 under coming to the par-4 18th on Sunday and it looked as though Smith was in the box seat when he landed his second shot on the green.
Neergaard-Petersen blocked his approach right and into the long rough between the bunkers.
But he conjured a miracle chip to 15 feet and nervelessly drained the par putt.
His Australian rival could do no better than three-putt from long range for bogey, allowing the Dane to triumph by a single shot.
Neergaard-Petersen had such a strong debut season on the DP World Tour that he secured his PGA Tour card for 2026.
"It's hard, I'm really at a loss for words - it's been a battle all day," said the 26-year-old.
"You know, even from the outside, sometimes you can look calm, but there was a storm inside all day today.
"But I managed to just keep battling, and then to get it up and down from there, to make that putt on the last."
The third member of the final group, Korean Si Woo Kim, bogeyed the last but held onto outright third spot at 13 under.
The 32-year-old Smith had a final round of two-under 69, with his long winless streak now dating back to LIV Golf Bedminster in August 2023.
Smith has won the Australian PGA Championship three times but has made no secret of the fact that - outside the majors - the Australian Open is the title he craves most.
Smith and Neergaard-Petersen went toe to toe on Sunday's back nine.
The Australian went ahead for the first time at the 10th hole, before the Dane levelled it up two holes later.
Neergaard-Petersen edged back into a one-shot lead at the 13th, only for Smith to tie it up again with a birdie on 14.
Both birdied the par-5 17th, with Smith making a clutch up and down after flaring his approach shot wide to the right.
The closest Smith has come to lifting the Stonehaven Cup was at Royal Sydney in 2016, when the Queenslander lost in a playoff to American Jordan Spieth.
South African Michel Hollick had the low round of the day with a six-under 65 to shoot up the leaderboard to outright fourth at 12 under, a shot clear of Australian Adam Scott.
After starting the final round right in contention for a second Stonehaven Cup, the 45-year-old Australian never really got going on Sunday as he signed for a one-under 70.
Tournament drawcard Rory McIlroy had a rollercoaster final day, mixing five birdies with three bogeys in a two-under 69 that left him in a tie for 14th at seven under.
The Northern Irishman will return to the sandbelt to play the 2026 Australian Open at nearby Kingston Heath.
Also in the group at seven under was Australian crowd favourite Min Woo Lee, who had a disappointing final round of three-over 74.
