Create a mixture of one-quarter cup ammonia and 3 cups warm water. Stir the ingredients and dampen a soft cloth.
Wipe down the countertops to remove any dirt, dust or debris. Dry the surface with a soft cloth to prevent streaks or watermarks.
Combine one-quarter cup boric acid powder, one-quarter cup baking soda, 3 cups warm water and one-half teaspoon lemon juice. Stir the ingredients until the boric acid powder, which is available in your grocery's laundry aisle, is completely dissolved.
Work the homemade abrasive cleaner into the rust stain with a plastic scouring pad. Continue to work the abrasive into the Corian countertop until the rust spot is completely removed.
Wipe down the Corian countertops with a damp cloth. Dry the countertop with a soft cloth to prevent watermarks and streaks.