The well-known experimentally observed sp-derived Au(111) Shockley surface states with Rashba spin splitting are perfectly fit by an effective tight-binding model, considering a two-dimensional hexagonal lattice with pz orbital and nearest-neighbor hopping only. The extracted realistic band parameters are then imported to perform the Landauer-Keldysh formalism to calculate nonequilibrium spin transport in a two-terminal setup sandwiching a Au(111) surface channel. Obtained results show strong spin density on the Au(111) surface and demonstrate (i) intrinsic spin-Hall effect, (ii) current-induced spin polarization, and (iii) Rashba spin precession, all of which have been experimentally observed in semiconductor heterostructures but not in metallic surface states. We therefore urge experiments in the latter for these spin phenomena.