We compute the diagonal isovector axial-vector as well as induced pseudoscalar form factors of nucleon, $Sigma$ and $Xi$ baryons by employing the light-cone QCD sum rules to leading order in QCD and including distribution amplitudes up to twist 6. Extrapolating our sum-rules results to low-momentum transfers, we make a comparison with experimental and lattice-QCD results where we can achieve a nice qualitative and quantitative agreement.