Kakitani gave Japan the lead in the 25th minute, receiving a pass from Toshihiro Aoyama and beating South Korean goalkeeper Jung Sung-ryong for his second goal of the tournament.
The hosts leveled in the 33rd on Yun Il-lok's strike from the top of the area past Japan's keeper Shusaku Nishikawa.
Kakitani scored again in the first minute of stoppage time, picking up a loose ball after Jung could only parry a shot from Genki Haraguchi.
Urawa Reds trio also did a good job throughout the competition.
Behind the victory, there was a disgusting battle outside the pitch between Japan and South Korea.
In the early part of the game, the Red Devils, a group of South Korean football supporters, hung a banner that read, "There is no future for people who have forgotten their past."
The message was apparently aimed at Japan's reluctance to acknowledge its militaristic and colonial past.
Along with the obviously political statement, large banners of two anti-Japan heroes were also displayed.
Korean independence activist An Jung-geun who assassinated Japan's first Prime Minister Ito Hirobumi in 1909, as well as Admiral Yi Sun-shin, leader of a successful naval campaign against their colonizers in the late 16th century.
But there was a nasty point in Japan side, as well.
Some Japanese fans waved the Rising Sun Flag, which many South Koreans consider a symbol of Japan's past militarism and imperialism.
The two countries were also at the center of a diplomatic row at the 2012 London Olympics when footballer Park Jong-woo held up a sign referring to a territorial dispute while celebrating South Korea's 2-0 win over Japan in the bronze medal game in August.
These crucial issues should have been kicked out of the football field, and I hope the two nations will come closer to each other in the near future.
Then, I'd like to admire South Korea's goal was really fantastic!!