Australia, headed to their fourth straight World Cup, grabbed the lead against the run of play in the 32nd minute when Robbie Kruse knocked a pass from the far post to an unmarked Mathew Leckie who tapped the ball in.
The victory over a Czech side that failed to qualify for the tournament in Russia was the first for the Socceroos outside Australia since a 1-0 win over the United Arab Emirates in Abu Dhabi in September 2016.
With a lack of goals a problem in Australia's qualifying campaign, Friday's attacking display gives the team's Dutch coach Bert van Marwijk plenty to think about before he pares four players from his 27-man squad by Monday's FIFA deadline.
Andrew Nabbout made his case for a World Cup role by scoring his first goal for Australia in the 54th minute when he won the ball on the right and his low, hard shot into the far corner beat Czech goalkeeper Tomas Koubek.
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Leckie and a Jakub Jugas own goal rounded out the win against a Czech side that had started brightly but failed to show much vigour after going behind.
Australia play a final warm-up against Hungary on June 9 before heading to Russia, where they face France, Denmark and Peru in Group C.
(Reporting by Michael Kahn, Editing by Christian Radnedge)
