Preheat the oven to 325°F (165°C). Lightly grease a 9-inch springform pan.
Combine crushed crackers with melted butter until evenly moistened. Press firmly into the bottom of the pan. Bake for 8–10 minutes, then cool completely.
In a large bowl, beat softened cream cheese until smooth. Add sugar and mix just until combined.
Add eggs one at a time, mixing slowly after each addition. Stir in sour cream and vanilla until smooth and creamy.
Pour the filling over the cooled crust and smooth the top.
Bake for 55–65 minutes, until the edges are set and the center jiggles slightly when shaken.
Turn off the oven, crack the door open, and let the cheesecake cool inside for 1 hour.
Remove and chill in the refrigerator for at least 4 hours or overnight.
For the topping, simmer cranberries, sugar, and liquid over medium heat until berries burst and the mixture thickens. Cool completely.
Spoon the cooled cranberry topping over the chilled cheesecake before serving.