Highly efficient single-material organic solar cells (SMOCs) based on fullerene-grafted polythiophenes were fabricated by incorporating electrospun one-dimensional (1D) nanostructures obtained from polymer chain stretching. Poly(3-alkylthiophene) chains were chemically tailored in order to reduce the side effects of charge recombination which severely affected SMOC photovoltaic performance. This enabled us to synthesize a donoracceptor conjugated copolymer with high solubility, molecular weight, regioregularity, and fullerene content. We investigated the correlations among the active layer hierarchical structure given by the inclusion of electrospun nanofibers and the solar cell photovoltaic properties. The results indicated that SMOC efficiency can be strongly increased by optimizing the supramolecular and nanoscale structure of the active layer, while achieving the highest reported efficiency value (PCE = 5.58%). The enhanced performance may be attributed to well-packed and properly oriented polymer chains. Overall, our work demonstrates that the active material structure optimization obtained by including electrospun nanofibers plays a pivotal role in the development of efficient SMOCs and suggests an interesting perspective for the improvement of copolymer-based photovoltaic device performance using an alternative pathway.