Turn the stove off and allow the surface to cool completely.
Fill a plastic zip bag with ice cubes. Place the bag of ice directly onto the melted plastic bag while it is still soft. Leave the ice bag in place until the plastic below it hardens. This should take about 20 to 30 minutes.
Remove the ice bag from the stove top surface. Gently scrape the hardened plastic bag off the stove top with a razor-edged scraper. Remove as much of the plastic as possible with the scraper.
Moisten a clean cloth with nail polish remover. Place the damp cloth onto the remaining melted plastic bag stain. Leave the cloth in place for up to 10 minutes or until the residue dissolves.
Lift the damp cloth off of the stove top. Use a razor-edged scraper to scrape the residue off the surface.
Dampen a sponge with warm water. Add one or two drops of dishwashing detergent to the wet sponge. Scrub the surface with the sponge, then rinse out the sponge and scrub it again with water only.
Dry the stove top surface with a dry cloth.