The San Antonio Spurs guard had 15 points in the third quarter to spark Australia's comeback. Matt Dellavedova made all three of his 3-point attempts in the period as Australia rallied from a 10-point halftime deficit.
Britain, which led by as many as 15 points in the third, trailed 66-60 at the end of the quarter.
But the run was not over.
Australia (2-2) started the fourth with an 18-0 run, which included a pair of Mills' 3-pointers.
Joel Freeland had 16 points for Britain, now 0-4 in its Olympic debut.