Spin accumulation is generated by passing a charge current through a ferromagnetic layer and sensed by other ferromagnetic layers downstream. Pure spin currents can also be generated in which spin currents flow and are detected as a nonlocal resistance in which the charge current is diverted away from the voltage measurement point. Here, we report nonlocal spin-transport on two-dimensional surface-conducting SrTiO3 (STO) without a ferromagnetic spin-injector via the spin Hall effect (and inverse spin Hall effect). By applying magnetic fields to the Hall bars at different angles to the nonlocal spin-diffusion, we demonstrate an anisotropic spin-signal that is consistent with a Hanle precession of a pure spin current. We extract key transport parameters for surface-conducting STO, including: a spin Hall angle of gamma approximate to (0.25 +/- 0.05), a spin lifetime of tau similar to 49 ps, and a spin diffusion length of lambda(s) approximate to (1.23 +/- 0.7) mu m at 2 K.