Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a muffin pan, or use paper liners.
In a small bowl, mix together applesauce, oil, and egg. In a large bowl, combine flour, sugar, baking soda, cinnamon, and salt. Make a well in the center, and pour in the egg mixture. Stir until just moistened. Fold in cranberries and pecans. Spoon into muffin cups, 2/3 full.
Bake in the preheated oven for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean. Cool in pan for 2 minutes before removing.