We report on a measurement of b-hadron lifetimes in the fully reconstructed decay modes B+→J/ψK+, B0→J/ψK∗(892)0, B0→J/ψK0s, and Λ0b→J/ψΛ0 using data corresponding to an integrated luminosity of 4.3  fb−1, collected by the CDF II detector at the Fermilab Tevatron. The measured lifetimes are τ(B+)=[1.639±0.009(stat)±0.009(syst)]  ps, τ(B0)=[1.507±0.010(stat)±0.008(syst)]  ps, and τ(Λ0b)=[1.537±0.045(stat)±0.014(syst)]  ps. The lifetime ratios are τ(B+)/τ(B0)=[1.088±0.009(stat)±0.004(syst)] and τ(Λ0b)/τ(B0)=[1.020±0.030(stat)±0.008(syst)]. These are the most precise determinations of these quantities from a single experiment.