Filling:
Preheat the oven to 325 degrees F.
In a mixing bowl, combine the ingredients with a fork until evenly moistened. Lightly coat the bottom and sides of an 8-inch springform pan with non-stick cooking spray.
Pour the crumbs into the pan and, using the bottom of a measuring cup or the smooth bottom of a glass, press the crumbs down into the base and 1-inch up the sides. Refrigerate for 5 minutes.
For the Filling:
In the bowl of an electric mixer, beat the cream cheese on low speed for 1 minute until smooth and free of any lumps. Add the eggs, 1 at a time, and continue to beat slowly until combined. Gradually add sugar and beat until creamy, for 1 to 2 minutes.
Add sour cream, lemon zest, and vanilla. Periodically scrape down the sides of the bowl and the beaters. The batter should be well-mixed but not overbeaten. Pour the filling into the crust-lined pan and smooth the top with a spatula.
Set the cheesecake pan on a large piece of aluminum foil and fold up the sides around it. Place the cake pan in a large roasting pan. Pour boiling water into the roasting pan until the water is about halfway up the sides of the cheesecake pan; the foil will keep the water from seeping into the cheesecake. Bake for 45 minutes. The cheesecake should still jiggle (it will firm up after chilling), so be careful not to overcook. Let cool in pan for 30 minutes. Chill in the refrigerator, loosely covered, for at least 4 hours. Loosen the cheesecake from the sides of the pan by running a thin metal spatula around the inside rim. Unmold and transfer to a cake plate.
Slice the cheesecake with a thin, non-serrated knife that has been dipped in hot water. Wipe dry after each cut.