Airport workers found the men on a navigational pier at the end of a runway last weekend.
The men tell the New York Post they rowed to the closest point on shore after overturning their kayak and losing a pair of paddles in Jamaica Bay.
It was the same runway where a man scaled a fence and walked into the airport after his personal watercraft ran out of gas in August 2012.
In both cases, the airport's $100 million Perimeter Intrusion Detection System of surveillance cameras and motion detectors failed to detect the men who climbed ashore.
Port Authority Police issued the kayakers summonses.