Keck-telescope spectrophotometry of the companion of PSR-J1810+1744 shows a flat, but asymmetric light-curve maximum and a deep, narrow minimum. The maximum indicates strong gravity darkening (GD) near the L1 point, along with a heated pole and surface winds. The minimum indicates a low underlying temperature and substantial limb darkening. The GD is a consequence of extreme pulsar heating and the near-filling of the Roche lobe. Light-curve modeling gives a binary inclination i=65.7{+/-}0.4. With the Keck-measured radial-velocity amplitude Kc=462.3{+/-}2.2km/s, this gives an accurate neutron star mass MNS=2.13{+/-}0.04M{sun}, with important implications for the dense-matter equation of state. A classic direct-heating model, ignoring the L1 gravitational darkening, would predict an unphysical MNS>3M{sun}. A few other "spider" pulsar binaries have similar large heating and fill factor; thus, they should be checked for such effects.