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 victory at the Khalifa Stadium.
"We played the entire tournament with great courage and always sought to impose our game," Japan coach Alberto Zaccheroni told reporters.
"We have a very young team. The bench players have made a big contribution, just as Lee did today."
Japan enjoyed long periods of possession on a windy, chilly night in Doha but Australia, seeking a first Asian Cup title, had the better chances with striker Harry Kewell proving wasteful in front of goal.
The Japanese were confident on the ball throughout yet played at a pedestrian pace by comparison to their previous matches. A higher tempo would perhaps have been more suitable against Australia's more experienced but slower side.
Without the influential Shinji Kagawa, who broke his foot in the semi-final, Japan selected Jungo Fujimoto as a replacement.
The midfielder, however, was ineffectual as the Blue Samurai failed to create many clear first-half openings.
Australia started the second period well and came close to taking the lead in the 48th minute when keeper Eiji Kawashima misjudged a centre that hit the crossbar and then Tim Cahill on the arm before Maya Yoshida hacked the ball off the line.
GLANCING HEADER
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 raced clean through and his low drive went straight to Kawashima.
Japan, who also played 120 minutes in their semi-final penalty shootout victory over South Korea on Tuesday, 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 breakthrough.
"We had opportunities but it is crucial to convert them and later that backfired on us. We needed to be more clinical," said coach Holger Osieck.
