The former champions were set to chase a modest 155-run target as a combined bowling effort restricted Scotland to 154/9 in the allotted 20 overs at the Grange Cricket Club Ground on Wednesday.
Opening batter George Munsey top-scored for the home side with a 16-ball 28, followed by wicketkeeper batter Matthew Cross (27), skipper Richie Berrington (23), and top-order batter Brandon McMullen (19).
Sean Abbott picked three wickets for Australia while Xavier Bartlett and Adam Zampa bagged two each.
Australia had an unwanted start to the run chase as they lost young opener Jake Fraser-McGurk (0) on just the third delivery of the innings.
Following his departure, Marsh joined Head in the middle and the duo combined to launch an astounding counterattack with belligerent hitting.
Travis Head was the core aggressor of the historic partnership as the left-handed opener conceded just 17 balls to reach half-century, the joint quickest by an Australian batter in the format.
The second-wicket partnership between Travis Head and Mitchell Marsh
The second-wicket partnership between Travis Head and Mitchell Marsh muscled Australia to 113/1 by the end of the batting powerplay, the highest score by a team in the history of T20Is.
Mark Watt gave Scotland a sigh of relief in the next over as he got rid of both Head and Marsh.
Marsh scored 39 off just 12 balls with the help of five fours and three sixes while Head remained the top-scorer for Australia with a 25-ball 80, peppered with 12 fours and five sixes.
Following their departure, wicketkeeper batter Josh Inglis alongside Marcus Stoinis anchored Australia to glory with 62 balls to spare.
Inglis remained unbeaten with a 13-ball 27 while Stoinis scored eight not out.
Mark Watt starred with the ball for Scotland, picking up key wickets of Travis Head and Mitchell Marsh and conceding just 13 runs in his two overs while the Australian batters decimated the rest.
Australia now leads Scotland 1-0 in the three-match T20I series with the remaining two fixtures scheduled on September 6 and 7 respectively at the same venue.