Preheat oven to 350º.
Coat bottom of a 9-inch round cake pan with 1 tablespoon melted butter; sprinkle brown sugar over butter. Drain apricots, reserving 1/2 cup liquid; pat apricots dry with paper towels. Arrange apricots, cut sides up, in pan.
Combine cake mix, egg, apricot liquid, lemon rind, and vanilla in a bowl. Beat with a mixer at medium speed 2 minutes.
Pour batter over apricots in pan.
Bake at 350º for 32 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 5 minutes on a wire rack. Loosen cake from sides of pan using a knife or narrow spatula; invert cake onto a plate.