For the crust: Preheat the oven to 350 degrees F. Wrap 3 layers of foil around the outside of a 9-inch-diameter springform pan with 3-inch-high sides. Butter the pan.
Combine the graham crackers, sugar and salt in a food processor and pulse until crumbly. Add the butter and pulse until moistened. Press the crumb mixture evenly onto the bottom and 1 1/2 inches up the sides of the prepared pan. Bake just until golden brown, about 15 minutes. Let cool completely.
Reduce the oven temperature to 325 degrees F.
For the filling: In an electric mixer fitted with the paddle attachment, beat the cream cheese on medium speed until fluffy. Add the sugar and vanilla and beat until combined. Add the eggs 1 at a time, mixing well after each addition. Add the sour cream and mix until smooth, about 35 seconds. Pour the filling into the cooled crust.
Set the cheesecake in a large baking pan. Add enough hot water to the baking pan to come 1 inch up the sides of the cheesecake pan. Bake until almost set (the center will move slightly when the pan is gently shaken) but not puffed, about 1 hour. Let cool at room temperature for 2 hours. Cover loosely with plastic wrap and refrigerate until completely cooled, preferably overnight or for at least 6 hours.
For the pomegranate sauce: Combine the pomegranate juice and sugar in a saucepan and cook over high heat until reduced to 1/2 cup, about 15 minutes. Let cool. Add the pomegranate seeds and mix to combine.
Pour the pomegranate sauce on top of the cooled cheesecake and serve.