The AFC Champions League side were still down in the 84th minute before staging a remarkable turnaround to grab all three points.
Kyoto's Brazilian midfielder Diego opened the scoring in the 58th minute and it looked as though the visitors would come away with a win before Kashima produced a miracle.
Ryuta Sasaki equalised in the 85th minute and then striker Shinzo Koroki broke the hearts of Kyoto with a goal a minute before time.
"We made a careless mistake to lose a goal and it made the game difficult, but my players never gave up until the end. It resulted in this victory," said Kashima's Brazilian coach Oswaldo Oliveira.
"We will have tough games this month, but my players have prepared very well for those games, so we are going to play together game by game."