Assemblies of disordered nanoparticles constitute an important class of materials that have numerous applications in energy conversion and storage, electronics, photonics, and sensing. One major roadblock that limits the widespread utilization of disordered nanoparticle assemblies (DNAs) is their poor damage tolerance; they fracture under small loads and, thus, have low toughness. The absence of fundamental understanding on the mechanical behavior and failure mechanism of disordered nanoparticle assemblies makes it even more challenging to develop new strategies to toughen these structures without compromising their mechanical strength. Here we show the formation of shear bands, highly localized regions of mechanical strain that prelude fracture, in disordered assemblies of spherical nanoparticles, which bear striking resemblance to the deformation mechanism of a different class of disordered materials, metallic glasses. We demonstrate that anisotropic nanoparticles greatly suppress shear band formation and toughen nanoparticle packings without sacrificing their strength, implying that tuning constituent anisotropy can be used to enhance toughness in disordered packings of nanoparticles.