The Boomers will now play the United States in the quarter-finals.
Mills had missed a similar shot with 25 seconds left, with Russia then taking the with two free throws to make it 80-79 with 4.1 seconds left.
But after a time out, Australia made one last play with Joe Ingles finding point guard Mills at the top of the key.
“'I had the mindset that if I was open I had to shoot, time was running down and I was glad that it went in,' Mills said.
“It's a good feeling. It's one of those shots I have always dreamt of making in the Olympic Games. It came off the guy's head so I had to catch the ball before I shot it."
Mills, who scored 39 points against Great Britain in the previous game, finished with 13. Hannah Davis and the women’s K4 crew finished sixth in the canoe sprint semi-final last night.
