Lee was afforded the freedom of the penalty area in the 109th minute to fire in a Yuto Nagatomo cross from the left as the Blue Samurai sealed a narrow victory at the Khalifa stadium.
Japan enjoyed long periods of possession on a windy, chilly night in Doha but Australia, seeking a first Asian title, had better chances with striker Harry Kewell proving wasteful in front of goal.
Japan looked confident with the ball throughout, yet played at a pedestrian pace by comparison to their previous matches.
Without the influential Shinji Kagawa, who broke his foot in the semifinal, Japan selected Jungo Fujimoto as a replacement. The midfielder, however, was ineffectual as Japan failed to create consequential clear openings.
Australia started the second half with a lot more promise and came within inches of taking the lead in the 48th minute when keeper Eiji Kawashima misjudged a cross that hit the crossbar and then Tim Cahill on the arm before Maya Yoshida hacked the ball off the line.
Japan striker Shinji Okazaki thought he had given his side the lead in the 66th minute but his glancing header went agonisingly wide of the far post after neat work down the left from Nagatomo. Kewell had a glorious chance to break the deadlock in the 71st minute when he went clean through and his low drive went straight to Kawashima.
Japan tired in the extra period as they went in search of a fourth Asian Cup after victories in 1992, 2000 and 2004. Australia substitute Robbie Kruse's strong header in the 105th minute was clawed out by Kawashima as the Socceroos pressed for a winner.
