Jones, who led by three strokes heading into Sunday, dropped three shots in his first two holes and triple-bogeyed the ninth but rallied to end eight under.
American Spieth, who missed an eagle putt on the last to force a play-off, carded a 71 to finish joint second.
He was joined on seven under by Scott, who shot a superb six-under 65.
The round of the day, though, came from another Australian, Rod Pampling, who made a 60-foot eagle putt on the 18th green for a course record 10-under 61 to earn him a fourth-place finish on six-under.
This bettered the 63 Spieth carded in the final round to win the title last year.
Despite the leader's poor start and two birdies of his own on the front nine, 22-year-old Spieth was unable to capitalise before Jones' two birdies on the back nine gave him the win.
"That was very stressful, it wasn't comfortable out there for me," said Jones, whose victory earns him a place in next July's Open Championship at Royal Troon.
"I've watched the Australian Open for many years and just to have my name on that trophy is something I'll never forget."
Joining Jones at next year's 145th British Open Championship will be fellow  Australians Pampling and Nick Cullen.
Cullen shot a 68 in his final round to share fifth place and earn the third qualifying place.
England's Lee Westwood carded his best round of the tournament - a two-under 69 - to finish tied for 18th on two under, while a 76 from Northern Ireland's Darren Clarke left him joint 30th on four over.

It took place in three areas in Deeside on Thursday following complaints that men had been held "virtual captives" for up to three years.
North Wales Police said the conditions they were living in were "utterly appalling".
The arrested man is local to the area and will be questioned by detectives.
Another man will be "voluntarily interviewed" at a later date.
Thursday's operation is part of a wider operation which aims to tackle serious and organised crime in north Wales, with a specific focus on human exploitation.
Det Ch Insp Neil Harrison said: "As a result of this morning's operation we have safeguarded, or simply put, freed, at least three people who are now being assessed."
A firearm, stolen property and a "significant amount of unaccountable cash" were also recovered and will form part of the investigation.
Ch Supt Sasha Hatchett, who oversaw the operation, said: "It is sometimes a common misconception that modern slavery is an issue for other parts of the world.
"The reality is that human trafficking exists right here on our doorsteps in communities across north Wales."
Matt Jones held off a challenge from world number one Jordan Spieth and fellow Australian Adam Scott to win the Australian Open by a shot.
[NEXT_CONCEPT]
Police have arrested a man for human trafficking offences and taken three people to a "place of safety" during a joint operation in Flintshire.