We demonstrate two-dimensional robust Raman cooling in a four-level tripod system, in which velocity-selective population transfer is achieved by a STIRAP pulse. In contrast to basic 2D Raman cooling with square envelope pulses [Phys. Rev. A 83, 023407 (2011)], the technique presented here allows for a wide variation in the pulse duration and amplitude once the adiabaticity criterion is satisfied. An efficient population transfer together with attaining of a narrow spread of the resonant-velocity group leads to the narrowing of the velocity-distribution spread down to 0.1vrec, corresponding to an effective temperature equal to 0.01Trec. This robust method opens new possibilities for cooling of neutral atoms.