Kina scored 10 points in the final overtime period as Navy (3-1) fought back from a five-point deficit.
William & Mary (1-3) took a 91-86 lead, but the Midshipmen (3-1) rallied to tie the score at 91.
David Schneider, who had a game-high 31 points for the Tribe, hit his second 3-pointer of the period to put William and Mary on top again.
Adam Teague, who tallied 18 for Navy, tied the score at 94 with his sixth 3-pointer.
The Tribe pulled ahead on two free throws by Schneider, who scored 11 in the final period.
Navy went on an 8-3 run to close out the game.
The Tribe's Danny Sumner, who had 30 points, hit a 3-pointer with six seconds left in regulation to push the game into overtime.