Russia had their first lead since midway through the fourth quarter when Vitaliy Fridzon went to the line and hit two free throws to make it 80-79 with 4.1 seconds left.
But Australia coach Brett Brown drew up one final play and they made it pay as Joe Ingles fed Mills at the top of the key and he drained the three to win it.
'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.
Australia had led 79-73 midway through the final quarter before Russia launched one last rally.
Andrei Kirilenko had struggled for much of the game, missing a dunk and seeing a number of lay-ups go in and out, but he came up with five quick points when it mattered, hitting two free throws and then returning to the line to complete a three-point play that made it 79-78 with 1:49 to go.
But Kirilenko then had to leave the game after taking a blow to the face when he lost the ball to Mills.
Australia could not take advantage, with David Andersen and Mills missing shots. That allowed Fridzon to give Russia the lead but they could not hold it as Mills struck.
Mills, who scored 39 points against Great Britain in the last game, finished with 13 today, leaving it to Ingles to lead Australia with 20 points.
Andersen had 13 points and Matt Dellavedova 10 with six rebounds and seven assists.
Sasha Kaun had 18 points for Russia, with new Minnesota Timberwolves pairing Kirilenko and Alexey Shved adding 13 each.
Russia had already sealed top spot in the group while Australia knew they could not improve on fourth place, with both teams advancing to the quarter-finals.
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