Preheat the oven to 350 degrees F. Lightly coat a muffin tin with cooking spray.
In a large bowl, whisk together the flour, baking soda, baking powder, salt and pumpkin pie spice.
In a separate bowl, combine the canned pumpkin, egg, applesauce, vanilla extract and maple syrup. Whisk well until combined.
Pour the pumpkin mixture into the flour mixture. Using a rubber spatula, stir the two mixtures until combined and no bits of flour are visible. Take care not to overmix.
Add the grated zucchini. Stir to combine.
Using a measuring cup or large cookie scoop, transfer the batter to the prepared muffin tin.
Bake until a toothpick inserted into the center of a muffin comes out clean, 16 to 18 minutes.
Let the muffins rest for about 10 minutes, then remove from the pan and cool on a wire rack. Serve or store in an airtight container.