The win meant little, however, with Russia (4-1) assured of top spot in Group B and Australia (3-2) sure to finish fourth and scheduled to face the heavily favoured United States team in the quarter-finals Wednesday.
Australia led for most of the game but Andrei Kirilenko had a three-point play and Mills missed a three-pointer with less than a minute to play. Vitaliy Fridzon made two free throws with four seconds on the clock to put Russia up 80-79.
But Mills got the ball at the top of the key and sank his winner.
Sasha Kaun led Russia with 18, and Alexey Shved and Kirilenko had 13 each. Kirilenko sat out the final minute with a cut above the left eye.