The fluctuation exchange approximation (FLEX) is used to model T_c versus strain in Sr₂RuO₄. Previously we showed that using first-principles parameters for band-structure, spin-orbit coupling and the orbital dependence of an atomically local electron-electron interaction, FLEX produces a state dominated by singlet, d_x²-y² pairing with smaller, spin-orbit-induced contributions in other channels (DOI: 10.1103/PhysRevLett.107.277003). While models based on triplet pairing were favored at that time, strong evidence has emerged for large or even dominant contributions from singlet pairing. Thus, FLEX, an approximation where electron-electron correlations are treated in a fully self-consistent manner, remains a useful tool for model studies to elucidate the nature of pairing in this compound. Indeed, our results show that FLEX accounts for the strain dependence of T_c  observed for Sr₂RuO₄. Namely, for a broad range of coupling strengths, we find that T_c  plummets when strain pushes a γ-band van Hove singularity through and below E_F.  At larger electon-electron coupling strengths, T_c  vs strain results are nearly flat from zero strain to the strain-induced dropoff. However, at small coupling strengths, consistent with T_c < 10K,  FLEX reproduces the experimentally observed enhancement in T_c with strain with a large peak in T_c before the dropoff. These results argue that the strain dependence is fully consistent with a pairing state dominated by singlet  d_x²-y²  contributions.