Air has a higher pressure when it's hotter, so it expands. When you place the glass on the plate, the air cools down and the pressure inside the glass drops. The paper towel prevents the air outside from getting in the glass to equate the pressure, so the pressure difference creates a net force that pushes the glass into the plate. It doesn't actually have anything to do with burning the oxygen, and the combustion also generates the same amount of carbon dioxide.