Make the Crust
Heat oven to 400° F. In a medium bowl, combine the graham cracker crumbs, sugar, and butter. Transfer to a 9-inch springform pan. Using a straight-sided dry measuring cup, press the mixture into the bottom and 2 inches up the sides of the pan. Bake until set, 8 to 10 minutes. Let cool.
Make and Chill the Filling
Sprinkle the gelatin over 1/4 cup boiling water. Let stand, stirring occasionally, until dissolved, about 5 minutes.
Using an electric mixer, beat the cream cheese until smooth. Mix in the pumpkin, sour cream, sugar, pumpkin pie spice, and vanilla. Mix in the gelatin mixture until incorporated.
Pour the mixture into the crust and refrigerate, covered, until firm, at least 2 hours and up to 2 days.