While the demonstrated power conversion efficiency of organic photovoltaics (OPVs) now exceeds 10%, new design rules are required to tailor interfaces at the molecular level for optimal exciton dissociation and charge transport in higher efficiency devices. We show that molecular shape-complementarity between donors and acceptors can drive performance in OPV devices. Using core hole clock (CHC) X-ray spectroscopy and density functional theory (DFT), we compare the electronic coupling, assembly, and charge transfer rates at the interface between C60 acceptors and flat- or contorted-hexabenzocorone (HBC) donors. The HBC donors have similar optoelectronic properties but differ in molecular contortion and shape matching to the fullerene acceptors. We show that shape-complementarity drives self-assembly of an intermixed morphology with a donor/acceptor (D/A) ball-and-socket interface, which enables faster electron transfer from HBC to C60. The supramolecular assembly and faster electron transfer rates in the shape complementary heterojunction lead to a larger active volume and enhanced exciton dissociation rate. This work provides fundamental mechanistic insights on the improved efficiency of organic photovoltaic devices that incorporate these concave/convex D/A materials.