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Preheat the oven to 350 degrees. Spray a 13- by 9-inch baking dish with cooking spray and set aside.
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Combine the cake mix, pumpkin puree, and remaining ingredients EXCEPT condensed milk in a bowl. Beat until smooth, about 2 to 3 minutes.
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Pour into the prepared cake pan, smooth the top, and bake 22 to 28 minutes, until a cake tester inserted into the center of the cake comes out clean.
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Set on a wire rack to cool for 10 minutes.
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After 10 minutes use the handle of a wooden spoon to poke holes about 3/4 of the way into the cake (you don’t want to poke through to the bottom). The holes should be about 1 inch apart.
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Pour the sweetened condensed milk as evenly as possible over the cake. Let the cake cool to room temperature, then cover loosely with plastic wrap and refrigerate for at least 6 hours (or overnight).