Three-times champions Japan, who won the shootout 3-0, will play the winners of Tuesday's second semi-final between Uzbekistan and Australia at the Khalifa Stadium in Saturday's showpiece.
Yasuyuki Konno scored the winning penalty on his 28th birthday after Koo Ja-cheol and Lee Yong-rae had their efforts saved by Kawashima, who had been criticised earlier in the tournament for some errors, and Hong Jeong-ho blasted wide.
"I told him a few days ago (Kawashima) that I trusted him and I told him again today and he did better than I even expected," Japan's Italian coach Alberto Zaccheroni told reporters.
The manner of the defeat proved too much for some Koreans who were in tears moments after they celebrated a 120th minute equaliser from Hwang Jae-won, who lashed home after a goalmouth scramble.
The east Asian rivals produced some of the best football of the tournament in the first 45 minutes at the Al Gharafa Stadium with Japan unlucky not to take the lead.
An eye-catching move in the 17th minute set Yuto Nagatomo clear down the left and the full-back's cross found Shinji Okazaki but his powerful header was deflected onto the inside of the post by keeper Jung Sung-ryong who then gathered the ball.
Despite the Blue Samurai's fast start it was Korea who took the lead five minutes later from the penalty spot in somewhat fortunate circumstances.
Konno was judged to have blocked Korea captain Park Ji-sung who, in his 100th international, was chasing a long ball into the area which he did not look like getting. Ki Sung-yueng tucked the spot-kick past Kawashima.
Japan did not let the decision affect them and they were level after another superb attacking move down the left.
Playmaker Keisuke Honda cut out three Korean defenders with a perfectly weighted through ball for Nagatomo and the full-back squared a cross which Ryoichi Maeda lifted over Jung for his third goal of the tournament.
The chances began to dry up in the second half with nerves likely having an effect on the two young sides as the tempo slowed with both teams switching to a more defensive style.
Extra-time looked to have provided a winner when Japanese substitute Hajime Hosogai powered home the rebound after Jung had saved Honda's poor penalty in the 97th minute.
Saudi Arabian referee Khalil Al Ghamdi had initially pointed for a free-kick before awarding Japan a penalty after Korea defender Hwang was judged to have obstructed forward Okazaki.
"I believe as human being referees can make mistakes, it was strange when referee pointed to outside of area but assistant pointed inside, but it is part of the game," Korean coach Cho Kwang-rae said.
