A numerical study is presented on the intrinsic viscosities of sheared dilute suspensions of nonspherical Brownian colloidal particles. The simulations confirm theoretical predictions on the intrinsic viscosities of highly oblate and highly prolate spheroids in the limits of weak and strong Brownian noise (i.e., for low and high Péclet numbers). Numerical data and fit functions are provided covering the entire shear-thinning regime, for spheroids ranging from highly oblate to highly prolate. The tumbling motion and intrinsic viscosities of a hemispherical cap and a helix are briefly discussed.