Cutting in from the left, the 21-year-old curled a rasping shot into the top corner to ensure the "Samurai Blue" qualified for their sixth successive World Cup.
It was some way to score a first goal for your country, with Ideguchi's strike adding to Takuma Asano's earlier goal scored at the end of the first half.
The victory means Japan now join the already qualified Brazil and Iran, along with hosts Russia, at the World Cup next June.
The defeat leaves Australia third in Asia's Group B, behind Saudi Arabia on goal difference. Ange Postecoglou's side play Thailand in their final match, while Saudi Arabia host Japan.
Whoever finishes third will face a playoff against a Group A team, with the winner then having to navigate an intercontinental playoff against an opponent from the CONCACAF region to reach Russia 2018.
Hope for Syria
Meanwhile, a brace from Omar Khribin helped Syria on their way to a 3-1 "home" victory against Qatar to keep their hopes of qualifying for the World Cup alive.
With the country still suffering the turmoil of a civil and international war, Syria's national team has been forced to play their home matches abroad.
So Thursday's match with Qatar was instead played in Malaysia -- 4,500 miles away from home.
Khribin's early goal was canceled out by Ali Assadalla, before the former put Syria back ahead 10 minutes into the second half.
An injury time goal by Mahmoud Al Mawas secured the win, pushing Syria into a playoff spot in Group A, just two points behind an automatic qualification place for Russia 2018.
With Iran having already qualified for the World Cup, South Korea is second in the group on 14 points, two ahead of Syria.
South Korea next play fourth-place Uzbekistan -- who are level with Syria in the group on 12 points, though they have an inferior goal difference -- in Tashkent on September 5, while Syria face Iran in Tehran.
The permutations in Group A are so tight that fifth-placed China, who play Qatar in their final qualifier, could still snatch that playoff spot.