The Australian striker opened the scoring for Grampus in the 28th minute before their Japanese counterparts Kawasaki Frontale equalised on the hour-mark then went ahead two minutes later through Kengo Nakamura and Juninho.
Kennedy’s goal ensured Grampus took an away goal into the second leg to be played in Nagoya next Wednesday although they lost the tie 2-1.
Grampus coach Dragan Stojkovic said his team were remaining hopeful of securing a place in the final four teams of the competition.
"The result is very active," he said. "We scored a goal away and that is very important for us. We have to be careful of Frontale using the counterattack, and we have to be aggressive. It will be a very interesting game."
Kennedy said he was unimpressed by Frontale’s physical tactics in which they tried to exert force on their opponents.
"I thought they came out with the intention to hurt or injure me, and anyone could see that in the first 20 or 30 minutes," Kennedy said. "It was pretty pathetic to be honest."