Breaking the match open in the third quarter, centre Ezi Magebegor and captain Jasmine Simmons helped turn what was a four-point lead into an 18-point game at the final change before the Aussies fully capitalised to win the second half 52-26.
Simmons scored eight of her 17 points in that devastating third period, using a combination of speed and silky finishing around the rim while Magbegor proved to be too much of a weapon in the paint, scoring 11 points to equal the Czech's output as a team for the quarter.
Australia's overall defence was again highly impressive, allowing the opposition to shoot at just 24% from the field and 2-22 (9%) from the three-point line.
Magbegor added to her impressive offensive game with an incredible six blocks, five of which came in the first period, while Jazmin Shelley harassed the Czechs out on the perimeter to collect three steals and a block.
It shaped as a close contest early in the game as the Czech Republic looked to be able to match Australia's size under the rim, cutting off the Sapphires' avenues to the basket with a 6-0 start.
Magbegor's defensive hustle brought the Aussies into the contest though and by the first break, the deficit was just a point.
That defence carried over into the second period and with the Sapphires pushing the ball up the floor quickly, the Czech's defensive structures began to crumble.
Shelley (ten points) and Monique Conti (six points, four assists) were able to slice through for easy lay-ups to help Australia to a three-point lead at half-time.
Simmons then notched her double-double early in the third quarter and as her and Kiera Rowe (nine points, six rebounds) helped the Sapphires to a 7-1 run, Australia had booked their place in the Semi-Final.
The Aussies will face the winner of France v USA on Friday night or early Saturday morning. Stay tuned to Basketball Australia's social media channels for updates and links to the live stream.
Click here for the full box score from the Quarter-Final while a replay can be viewed via FIBA below.