Czech Republic have failed to qualify for the 2018 World Cup, but Australia will be present at this summer's tournament, and were impressive in their penultimate international friendly before opening their World Cup campaign against France on June 16.
Against the run of play, Leckie sent Australia ahead in the 32nd minute of action, with the 27-year-old turning a low Robbie Kruse cross into the back of the net.
Australia then doubled their advantage in the 54th minute when Andrew Nabbout capitalised on a mistake from the Czech defence. Indeed, the attacker worked some space inside the penalty box before finishing past Tomas Koubek for his first international goal.
Aaron Mooy played a key role in Australia's third of the match in the 72nd minute, with the Huddersfield Town midfielder winning the ball in a deep position before surging forward and picking out Leckie, who finished into the back of the net for his second goal.
The victory was Australia's first in three games under new head coach Bert van Marwijk, and the Socceroos will now switch their attention to next weekend's international friendly with Hungary.
AUSTRALIA (4-3-3): Ryan; Behich, Sainsbury, Milligan, Risdon (Degenek 76'); Mooy, Rogic (Irvine 66'), Luongo; Kruse (Petratos 73'), Nabbout (Maclaren 61'), Leckie (Arzani 84')
CZECH REPUBLIC (4-3-3): Koubek; Boril, Kalas, Jugas, Novak; Husbauer, Barak (Sykora 57'), Darida; Schick (Sural 75'), Krmencik (Krmencik 46'), Kopic (Horava 83')