Quantum dot solar cells (QDSCs) with hexagonal fullerene nanosheets (C60-NS) embedded in a titanium oxide/cadmium sulfide (TiO2/CdS) photoanode coupled with a carbon-cloth (C-cloth) coated with molybdenum sulfide (MoS2) counter electrode (CE) are studied for the first time. C60-NS due to a favorable work function of 4.57 eV and a conductance of 1.44 μS, enable faster electron injection from the conduction band of cadmium sulfide to the current collector, in contrast to the bulk fullerene based TiO2/CdS solar cell. The champion cell with the TiO2/C60-NS/CdS photoanode and a MoS2/C-cloth CE exhibits a high power conversion efficiency of 5.6%, greater by ∼14% relative to its' analogue cell with bulk fullerene. A large area cell of 1 cm2 dimensions with TiO2/C60-NS/CdS gives a PCE of 2.9%. The effect of MoS2 in improving the efficiency of the cell with a TiO2/C60-NS/CdS photoanode is realized in terms of enhanced electrocatalytic activity for polysulfide reduction, and lower charge transfer resistance at the polysulfide/CE interface compared to a cell with the same photoanode but having pristine carbon-cloth as the CE. The ability of MoS2 for catalyzing the oxidized polysulfide species at the CE and C60-NS for improving the charge collection at the photoanode serve as indicators for their wider utilization in solar cells. It also serves as a good supercapacitor material. A MoS2/C-cloth based symmetric cell exhibits a specific capacitance of 645 F g-1 at 2 A g-1, which shows its' potential for energy storage as well. By integrating the QDSC and the supercapacitor, the resulting integrated device acquires a photovoltage of 0.7 V, under 1 sun illumination. © 2018 The Royal Society of Chemistry.