This invention provides a method and apparatus for closing the eyelids of persons suffering from nocturnal lagophthalmos (the inability to close the eyelids when sleeping), so as to keep their eyes moist and to protect their eyes from contacting the bedding while they sleep. The method is to apply gentle pressure on the inner ends of the eyelids with soft fingerlike protrusions affixed to a support that spans the nose and is held in place by adjustable, elastic headbands. This pressure pulls the eyelids towards the nose, which forces the eyelids to close and stay closed, thereby preventing loss of tear fluids by evaporation. In one embodiment, pressure can also be applied to the nasolacrinal drainage system to prevent tear fluids from draining out of the eye into the nasal cavity.