Membrane technology is a dynamically developing field of separation science that is poised to result in new and efficient processes, energy and cost savings, and sustainability benefits. A key challenge in this field is the development of highly selective membranes, which can be addressed by the development of mixed-matrix membranes (MMMs) containing fillers such as metal–organic frameworks (MOFs). However, the lack of interfacial adhesion causes nanosized gaps between the filler and the polymer matrix. In this study, we aim to elucidate the intrinsic properties of MMMs and bridge the gap between their material constituents. A series of novel membranes comprising MOF nanoparticles with similar chemical and morphological properties but increasing pore size (UiO-66–68-NH2) were prepared. The nanoparticles’ surface was covalently grafted with poly(N-isopropylacrylamide) (PNIPAM) chains, which could then become entangled with the membranes’ polymer matrix. Morphological characterization and organic solvent nanofiltration tests revealed that membranes with PNIPAM-grafted fillers do not suffer from the formation of pinholes at the filler–matrix interface that are detrimental to the filtration performance. For the first time, the experimental results showed an excellent match with a predictive model of nanofiltration built around the premise of liquid transport through the highly ordered pores of the MOF filler.