Glass surfaces are contaminated by exposure to overheated oleic acid vapor and then cleaned by low-pressure plasma of a dc glow discharge in either air or argon. In this study, the oleic acid is used as model for hydrophobic organic contaminant and glass as a model for inorganic hydrophilic substrate. The processes of contamination and plasma cleaning are studied by atomic force microscopy (AFM), which revealed formation of oleic acid nanodroplets during contamination and, then, their removal during a few minutes of plasma cleaning. Water contact angle measurements show a much faster effect of plasma cleaning treatment, the contaminated surface changing from slightly hydrophobic to superhydrophilic in less than 30s. This effect can be attributed to oxidation and hydroxylation of the oleic acid, as indicated by infrared absorption measurements. Also, the AFM indentation of the oleic acid nanodroplets after short plasma treatment indicates solidification of the remnant contaminant material.