Approximately one-third of the human proteome is made up of proteins that are entirely disordered or that contain extended disordered regions. Although these disordered proteins are closely linked with many major diseases, their binding mechanisms with small molecules remain poorly understood, and a major concern is whether their specificity can be sufficient for drug development. Here, by studying the interaction of a small molecule and a disordered peptide from the oncogene protein c-Myc, we describe a "specific-diffuse" binding mechanism that exhibits sequence specificity despite being of entropic nature. By combining NMR spectroscopy, biophysical measurements, statistical inference, and molecular simulations, we provide a quantitative measure of such sequence specificity and compare it to the case of the interaction of urea, which is diffuse but not specific. To investigate whether this type of binding can generally modify intermolecular interactions, we show that it leads to an inhibition of the aggregation of the peptide. These results suggest that the binding mechanism that we report may create novel opportunities to discover drugs that target disordered proteins in their monomeric states in a specific manner.