Jones had a three-shot lead heading into the final round at the Australian Golf Club in Sydney, but a two-over 73 almost saw his second PGA Tour title slip away.
The Australian was three over for his round after two holes, a bogey on the first immediately followed by a double at the first par three.
Jones recovered with two birdies, but a triple-bogey seven on the ninth left him with work to do on the back nine.
But he picked up two shots on his way in to claim victory by one stroke from major winners Scott and Spieth.
Jones said: "I got the job done. There was a lot of stress and a lot of anxious moments, but I came through with that lipping putt on the last to get the trophy.
"To have my name on the this trophy with (Jack) Nicklaus, (Jack) Newton, (Greg) Norman, all those guys, is a dream come true for me and something that can never be taken away."
Scott started the day nine shots off the pace, but ended just one stroke behind after picking up seven birdies in his six-under 65.
Spieth bogeyed three of the first six holes, but fought back to finish evens for the day to join Scott in second.
The 2014 Masters and US Open champion also saw his course record surpassed.
Australian veteran Rod Pampling went two better than the mark Spieth set last year with a 10-under 61 to finish two shots off the pace.
The 46-year-old, who eagled the last to set a new mark, said: "It was one of those where at the end things started to go in and that putt on the last was just one of those one in a million that was due to go in."