The Wallabies have clinched a heart-stopping 16-15 victory to end their Murrayfield misery and snap a three-game losing streak against Scotland.

Blair Kinghorn had the chance to win it for the home side in the final minute of Saturday's (Sunday AEDT) clash in Edinburgh but the five-eighth's penalty attempt sailed wide.

The Australians hadn't won at the famed ground since 2016, with the victory a massive morale boost as they open their tough five-Test tour.

While they were able to break their hoodoo, it wasn't a pretty performance by the visitors.

They talked pre-match about their discipline, yet conceded 15 penalties with Taniela Tupou pinged at the breakdown to give Kinghorn his winning opportunity.

Wallabies coach Dave Rennie admitted he was "relieved" that they had hung on for the victory.

"We got ourselves in a bit of a hole after half-time, an opportunist try and we're down 15-6 but the boys showed a lot of character and fought hard for each other and managed to hang on," Rennie said.

"We've worked really hard and it's pleasing to get the tour off with a win.

"We've got a lot more in us — we need to be a hell of a lot more clinical when we're down their end as we had plenty of opportunities."

The Australians struggled with Scotland's ferocity at the breakdown early on despite the best efforts of Michael Hooper, who was back in the line-up for the first time after a three-month mental health break.

Scotland opened the try-scoring when full-back Ollie Smith showed his footwork to dot down in the 11th minute.

But Australia took a 6-5 half-time lead with Bernard Foley landing a 41st-minute penalty.

The Scots raced ahead early in the second half through a brilliant Kinghorn try.

Off a Wallabies loose pass, Kinghorn toed the ball ahead and then kicked again, with the ball bouncing into the rangy playmaker's hands to touch down.