The first observation of the Ξb0→J/ψΞ−π+ decay and the most precise measurement of the branching fraction of the Λb0→J/ψΞ−K+ decay are reported, using proton-proton collision data from the LHCb experiment collected in 2016–2018 at a centre-of-mass energy of 13TeV, corresponding to an integrated luminosity of 5.4fb−1. Using the Λb0→J/ψΛ and Ξb−→J/ψΞ− decays as normalisation channels, the ratios of branching fractions are measured to be B(Λb0→J/ψΛ)B(Λb0→J/ψΞ−K+)B(Ξb−→J/ψΞ−)B(Ξb0→J/ψΞ−π+)=(1.17±0.14±0.08)×10−2,=(11.9±1.4±0.6)×10−2, B ( Λ b 0 → J / ψ Ξ - K + ) B ( Λ b 0 → J / ψ Λ ) = ( 1.17 ± 0.14 ± 0.08 ) × 10 - 2 , B ( Ξ b 0 → J / ψ Ξ - π + ) B ( Ξ b - → J / ψ Ξ - ) = ( 11.9 ± 1.4 ± 0.6 ) × 10 - 2 , where the first uncertainty is statistical and the second systematic.