Anosike missed just one shot from the field (6 of 7) and converted 5 of 8 free-throw attempts after missing nine of 11 free throws in the Saints’ season opener against Vermont.
Siena (1-1) got its largest lead of the game when Evan Hymes sank two free throws to put the Saints up 47-41 with 1:00 to play.
But Tilman Dunbar knocked down two consecutive jumpers for Navy (1-1) and Jerome Alexander made a shot with 20 seconds remaining to send the game into overtime.
Both teams shot poorly in the extra period, as Navy missed all eight field-goal attempts during the period and Anosike accounted for Siena’s lone made field goal.
Siena knocked down 5 of 6 free throws in overtime to seal the win.