  It has been suggested that non-relativistic outflows from quasars can
naturally account for the missing component of the extragalactic $\gamma$-ray
background and explain the cumulative neutrino background through pion decay in
collisions between protons accelerated by the outflow shock and interstellar
protons. Here we show that the same quasar outflows are capable of accelerating
protons to energies of $\sim 10^{20}$ eV during the early phase of their
propagation. The overall quasar population is expected to produce a cumulative
ultra high energy cosmic ray flux of $\sim10^{-7}\,\rm
GeV\,cm^{-2}s^{-1}sr^{-1}$ at $E_{\rm CR}\gtrsim10^{18}$ eV. The spectral shape
and amplitude is consistent with recent observations for outflow parameters
constrained to fit secondary $\gamma$-rays and neutrinos without any additional
parameter tuning. This indicates that quasar outflows simultaneously account
for all three messengers at their observed levels.
