We explore the second order bilinear magnetoelectric resistance (BMER) effect in the d-electron-based two-dimensional electron gas (2DEG) at the SrTiO_{3}(111) surface. We find evidence of a spin-split band structure with the archetypal spin-momentum locking of the Rashba effect for the in-plane component. Under an out-of-plane magnetic field, we find a BMER signal that breaks the sixfold symmetry of the electronic dispersion, which is a fingerprint for the presence of a momentum-dependent out-of-plane spin component. Relativistic electronic structure calculations reproduce this spin texture and indicate that the out-of-plane component is a ubiquitous property of oxide 2DEGs arising from strong crystal field effects. We further show that the BMER response of the SrTiO_{3}(111) 2DEG is tunable and unexpectedly large.