We report on a measurement of the flavor-specific B_{s}^{0} lifetime and of the D_{s}^{-} lifetime using proton-proton collisions at center-of-mass energies of 7 and 8 TeV, collected by the LHCb experiment and corresponding to 3.0 fb^{-1} of integrated luminosity. Approximately 407 000 B_{s}^{0}→D_{s}^{(*)-}μ^{+}ν_{μ} decays are partially reconstructed in the K^{+}K^{-}π^{-}μ^{+} final state. The B_{s}^{0} and D_{s}^{-} natural widths are determined using, as a reference, kinematically similar B^{0}→D^{(*)-}μ^{+}ν_{μ} decays reconstructed in the same final state. The resulting differences between widths of B_{s}^{0} and B^{0} mesons and of D_{s}^{-} and D^{-} mesons are Δ_{Γ}(B)=-0.0115±0.0053(stat)±0.0041(syst) ps^{-1} and Δ_{Γ}(D)=1.0131±0.0117(stat)±0.0065(syst) ps^{-1}, respectively. Combined with the known B^{0} and D^{-} lifetimes, these yield the flavor-specific B_{s}^{0} lifetime, τ_{B_{s}^{0}}^{fs}=1.547±0.013(stat)±0.010(syst)±0.004(τ_{B}) ps and the D_{s}^{-} lifetime, τ_{D_{s}^{-}}=0.5064±0.0030(stat)±0.0017(syst)±0.0017(τ_{D}) ps. The last uncertainties originate from the limited knowledge of the B^{0} and D^{-} lifetimes. The results improve upon current determinations.