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 rough between the bunkers.
But he conjured a miracle chip to 10 feet and nervelessly drained the putt.
His rival could do no better than three-putt from long range for bogey, allowing the Dane to triumph by a single shot.
The 32-year-old Smith had a final round of two-under 69, with his 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 the most.
Korean Si Woo Kim bogeyed the last but held onto outright third at 13 under.
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.
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.
