A fundamental question in molecular evolution is how protein functional differentiation alters the ability of cells and organisms to cope with stress and survive. To answer this question we used two paralogous Hsp70s from mouse and explored whether these highly similar cytosolic molecular chaperones, which apart their temporal expression have been considered functionally interchangeable, are differentiated with respect to their lipid-binding function. We demonstrate that the two proteins bind to diverse lipids with different affinities and therefore are functionally specialized. The observed lipid-binding patterns may be related with the ability of both Hsp70s to induce cell death by binding to a particular plasma-membrane lipid, and the potential of only one of them to promote cell survival by binding to a specific lysosomal-membrane lipid. These observations reveal that two seemingly identical proteins differentially modulate cellular adaptation and survival by having acquired specialized functions via sequence divergence. Therefore, this study provides an evolutionary paradigm, where promiscuity, specificity, sub- and neo-functionalization orchestrate one of the most conserved systems in nature, the cellular stress-response.