His try sent the home crowd into a stunned silence - for 75 minutes they'd been on top but ultimately a two-try performance from outside centre Huw Jones went unrewarded.
The victory evoked memories of last year's controversial, last minute World Cup quarter-final in which a Foley penalty goal secured Australia's passage to the semis.
Israel Folau was among Australia's best in a superb display in his 50th Test.
However it looked like things may be over for Australia when Skelton was shown a yellow card for a crude clear-out on Scotland's Johnny Gray.
"You never like to go a man down but we've been in that situation before," Wallabies skipper Stephen Moore said.
"I was proud of the effort, the boys dug in there. There's positive signs.
"It was too close for comfort there. I'm proud of the effort - we stuck in there in the second half.
"Scotland are always so tough here. We have a lot of respect for them"
Australia fell behind 10-0 after a horror opening ten minutes of play in which Scotland skipped away to an early lead and Michael Cheika's lineout general Adam Coleman went off with a knee injury.
Coleman suffered the injury in the fifth minute when his left knee was hit awkwardly during a ruck, and he was replaced by Rob Simmons.
Soon after, Scotland's Stuart Hogg burst onto a midfield chip kick - narrowly beating Australia's Henry Speight to the ball - before scampering away for the game's opening try after eight minutes.
By the time Coleman returned to the bench on crutches after 22 minutes, the Wallabies had levelled the scores by way of a superb converted try to Reece Hodge and a penalty goal from Bernard Foley.
Hodge finished off a terrific backline play which started with a wraparound between Folau and Foley, who put Dane Haylett-Petty into space before offloading to Hodge - who dummied past Scotland No.15 Stuart Hogg and carried a defender over the line.
But Australia's joy was short-lived, and Scotland again claimed a well-deserved advantage when in the 27th minute Hogg bagged his second by breaking weak tackles from Kuridrani and Haylett-Petty.
The home side were given a standing ovation from a packed crowd of 65,395 as they went to the sheds leading 17-10 at the main break.
They certainly would've received another one at fulltime, if not for Kuridrani's late heroics.
- AAP