Antlers coach Jorginho, a World Cup winner with Brazil in 1994, became the first man to win the competition as a manager and player after lifting the trophy with Kashima in 1997.
"These kinds of opportunities don't come along very often," the 48-year-old told reporters. "I feel very privileged. I hope I can achieve the same thing in the league and Emperor's Cup."
Jorginho is in his first season as manager of Kashima, having taken over the team from countryman Oswaldo de Oliveira after he returned to Brazil to coach Botafogo.
Midfielder Shibasaki gave Kashima the lead with a penalty after 73 minutes only for Genki Omae to equalise from the spot four minutes later in front of 45,000 at the National Stadium.
Shibasaki settled matters three minutes into extra time, smashing the ball home after manufacturing space to shoot with a clever piece of skill.
"I just hit it," said the 20-year-old man of the match, whose double strike gave Kashima a fifth J-league Cup title.
"I was lucky to get the ball under control and get the shot in. It was fantastic to see it go in."
- Sports & Recreation