We present clear evidence for the motion of the companion star in the low-mass X-ray binary (LMXB) X1822-371. We detect N III λ4640 emission moving in antiphase with the radial velocity curve of the neutron star and produced on the X-ray-heated hemisphere of the donor star. From the motion of this feature we derive a lower limit to the radial velocity semiamplitude of the companion star, K2>=300+/-8 km s-1, which, combined with a previous determination of the inclination angle and the pulsar's radial velocity curve, yields M2>=0.36(2)Msolar and M1>=1.14(6)Msolar. The He I λ4471 absorption line moves at lower velocities (~=225 km s-1) and with a -0.05 phase shift, suggesting a likely origin on the gas stream near the L1 point. In addition, we detect an S-wave emission of O VI λ3811 produced by illumination of the hot spot bulge by the central source. The Balmer lines are dominated by broad absorptions probably due to obscuration of the accretion disk by vertically extended cool material from the splash region and overflowing stream. We also derive a more accurate, and significantly different (compared to earlier work), systemic velocity of γ=-44+/-5 km s-1, based on the motion of the He II λ4686 wings and Doppler tomography. This work confirms the power of imaging the companion stars in LMXBs and outbursting transients using the Bowen fluorescence transitions.