Various large-scale experiments for double beta decay or dark matter are based on xenon. Current experiments are on the tonne scale, but future ideas also aim for even larger sizes. Here we study the potential of the isotope ¹³¹Xe to allow real-time capture measurements of solar pp-chain neutrinos, besides classical neutrino-electron scattering. Here we use improved nuclear-structure calculations to determine the cross sections of solar neutrinos on ¹³¹Xe. Our updated capture-rate estimate is (80 ± 22) SNU, with neutrino survival probabilities taken into account. According to our calculations, the ⁸B neutrinos are the dominant contribution to the total capture rate. Due to our more accurate treatment of the phase-space factor the computed capture rate, (60 ± 19) SNU, is significantly larger than what was expected based on previous calculations. This improves considerably the prospects of real-time monitoring of pp-chain neutrinos for long periods of time.