The Boomers sealed a sixth consecutive victory in the tournament to make history at the Shanghai Oriental Sports Center on Wednesday.
Australia took charge in the third quarter, outscoring the Czechs by 30 points to 18 to seize control and went on to set up a last-four showdown with Spain in Beijing on Friday.
Mills, Chris Goulding and Andrew Bogut played key roles for Andrej Lemanis' side, scoring 48 points between them to ensure a brilliant performance from Tomas Satoransky was in vain.
Satoransky sunk 13 points, laid on 12 assists and claimed nine rebounds, while Patrik Auda racked up 21 points in defeat for the Czechs.
Point guard Mills shot nine of 15 from the field as he bagged a game-high 24 points, grabbing four rebounds and providing six assists in an influential display.
Goulding and Bogut – on court for just over 12 minutes – finished with 14 and 10 points respectively.
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Photo Getty Images Caption: Australia celebrate reaching the FIBA World Cup semi-finals