Anti-perovskites A₃SnO (A = Ca, Sr, and Ba) are an important class of materials due to the emergence of Dirac cones and tiny mass gaps in their band structures originating from an intricate interplay of crystal symmetry, spin-orbit coupling, and band overlap. This provides an exciting playground for modulating their electronic properties in the two-dimensional (2D) limit. Herein, we employ first-principles density functional theory (DFT) calculations by combining dispersion-corrected SCAN + rVV10 and mBJ functionals for a comprehensive side-by-side comparison of the structural, thermodynamic, dynamical, mechanical, electronic, and thermoelectric properties of bulk and monolayer (one unit cell thick) A₃SnO anti-perovskites. Our results show that 2D monolayers derived from bulk A₃SnO anti-perovskites are structurally and energetically stable. Moreover, Rashba-type splitting in the electronic structure of Ca₃SnO and Sr₃SnO monolayers is observed owing to strong spin-orbit coupling and inversion asymmetry. On the other hand, monolayer Ba₃SnO exhibits Dirac cone at the high-symmetry Γ point due to the domination of band overlap. Based on the predicted electronic transport properties, it is shown that inversion asymmetry plays an essential character such that the monolayers Ca₃SnO and Sr₃SnO outperform thermoelectric performance of their bulk counterparts.