Travis Head, fresh from his hundred in Wednesday's opener, was out for a first-ball duck after Scotland won the toss at the Grange.
But his exit brought Leeds-born wicketkeeper Inglis to the crease, with the number three smashing seven fours and as many sixes as he raced to three figures in just 43 balls, the fastest hundred for Australia in men's T20s.
Inglis's innings was the cornerstone of Australia's 196-4, with Scotland managing just 126 all out in reply.
"It's pretty special, to be honest," Inglis said after stumps. "To hold that record is really nice.
"There was a bit happening (on the pitch) early doors," he said.
"Once the new ball wore off, it got easier. I was just looking to play some good shots and show some intent.
"It's a good opportunity for me to get some game time and try to cement my spot. There's a lot of good players but to put some performances on the board is pretty key."
Opening batsman Head was bowled for a golden duck by Brad Currie, the paceman leading Scotland's attack with 3-37.
But there was no stopping Inglis as he powered his way to a century before he was caught in the covers off Chris Sole.
Scotland's chase never got going, with Brandon McMullen playing a lone hand of 59 as Australia all-rounder Marcus Stoinis took 4-23.
