The high-spin structures and isomers of the N=81 isotones 135Xe and 137Ba are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. Both nuclei are populated (i) in 136Xe+238U and (ii) 136Xe+208Pb MNT reactions employing the high-resolution Advanced Gamma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA, (iii) in the 136Xe+198Pt MNT reaction employing the γ-ray array GAMMASPHERE in combination with the gas-detector array CHICO, and (iv) via a 11B+130Te fusion-evaporation reaction with the HORUS γ-ray array at the University of Cologne. The high-spin level schemes of 135Xe and 137Ba are considerably extended to higher energies. The 2058-keV (19/2−) state in 135Xe is identified as an isomer, closing a gap in the systematics along the N=81 isotones. Its half-life is measured to be 9.0(9) ns, corresponding to a reduced transition probability of B(E2,19/2−→15/2−)=0.52(6) W.u. The experimentally deduced reduced transition probabilities of the isomeric states are compared to shell-model predictions. Latest shell-model calculations reproduce the experimental findings generally well and provide guidance to the interpretation of the new levels.