Antwoine Anderson added 14 points for the Kings who jumped out to a 14-5 lead in the first quarter and never trailed.
BK led by 11 at the half, but New Rochelle made their run in the third quarter, cutting the lead to only three points after three quarters. Joe Clarke was a big reason New Rochelle hung in the game. He scored 26 of the team's 39 points.
Kearney opened the fourth quarter with a 7-2 spurt to take a 41-33 advantage. A Clarke bucket got New Rochelle to 41-37, but the Kings made enough free throws down the stretch to earn a trophy.
It's the second state title for the Kearney boys. BK's girls team also won a state championship Sunday, making Kearney the first Section V school to win both finals in the same season. The Kings are the first school anywhere in New York to win both since 1981.