Disordered nanoparticle assemblies constitute an important class of materials that have numerous applications in energy conversion and storage, electronics, photonics, and sensing. Unfortunately, however, such assemblies tend to fracture and abrade under small loads, significantly limiting their widespread use. In this work, we show that anisotropic nanoparticles greatly enhance the toughness of disordered nanoparticle packings by suppressing shear band formation. Our results imply that constituent anisotropy can be tuned to enhance toughness in disordered packings.