Behich bundled the ball over his own goal line after Takuma Asano's late shot looped up and hit the post, ensuring Australia missed out on a 12th straight win on the road to Qatar 2022.
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Ao Tanaka had given Japan the lead in the ninth minute as the home side sought to pick up only their second victory after four games in the final phase of the continent's qualifying campaign, a run that put coach Hajime Moriyasu under pressure.
The result moves third-placed Japan to within three points of the Socceroos, who lead Group B ahead of Saudi Arabia -- also on nine points but with a game in hand -- in the battle for two guaranteed places from the section at next year's World Cup.
But Ajdin Hrustic levelled the scores 20 minute from time with a curling free kick that went in off the underside of Shuichi Gonda's crossbar after VAR had overturned a decision to award the Australians a penalty.
The Japanese, who have qualified for every World Cup since 1998, were under huge pressure going into the game having won only one of their previous matches in the final phase of Asia's preliminaries.
Moriyasu rung the changes, dropping Shibasaki -- who was responsible for the goal Japan conceded against Saudi Arabia last week -- and replacing him with the more dynamic Tanaka.
The change paid off in the ninth minute as Tanaka was found with time and space in the penalty area by Takumi Minamino, and the midfielder scored with a low shot past Ryan.
Aaron Mooy and Tom Rogic went close before Hrustic was brought down on the edge of the area by Hidemasa Morita and, after referee Abdulrahman Al Jassim had initially awarded a penalty, VAR overturned the decision and gave a free kick.
It mattered little as Hrustic struck in style before Ryan kept a determined Japan at bay until Behich's own goal.
Only the top two teams in each of Asia's two qualifying groups advance automatically to the finals, with the third-placed teams going into a series of playoffs.