Jedinak might argue he deserved to be credited with the hat-trick, but the official scorer ruled his first effort an own goal after it deflected off a defender.
Honduras' Bryan Acosta, who escaped a handful of yellows throughout the match, was eventually pinged for handball inside the box.
Alberto Elis netted an injury time consolation goal for the visitors.
Nevertheless, the coach's future remains uncertain after he was heavily linked with the exit regardless of the Socceroos' qualification fate.
Honduras lost Emilio Izaguirre to injury before the break and his replacement, Henry Figueroa, was involved in the Socceroos' opener.
The Australians defeated Honduras 3-1 in Sydney in a game which would book the victor a place in the world's greatest sporting tournament.
It proved to be a memorable night for captain Mile Jedinak, who scored all three of Australia's goals, in the 53rd, 72nd and 85th minutes.