Water (H2O), one of the most ubiquitous molecules in the universe, has bright millimeter-wave emission lines that are easily observed at high redshift with the current generation of instruments. The low-excitation transition of H2O, p-H2O(2(0,2) - 1(1,1)) (nu(rest) = 987.927 GHz), is known to trace the far-infrared (FIR) radiation field independent of the presence of active galactic nuclei (AGNs) over many orders of magnitude in FIR luminosity (L-FIR). This indicates that this transition arises mainly due to star formation. In this paper, we present spatially (similar to 0 ''.5 corresponding to similar to 1 kiloparsec) and spectrally resolved (similar to 100 kms(-1)) observations of p-H2O(2(0,2) - 1(1,1)) in a sample of four strong gravitationally lensed high-redshift galaxies with the Atacama Large Millimeter/submillimeter Array. In addition to increasing the sample of luminous (>10(12) L-circle dot) galaxies observed with H2O, this paper examines the L-H2O/L-FIR relation on resolved scales for the first time at high redshift. We find that L-H2O is correlated with L-FIR on both global and resolved kiloparsec scales within the galaxy in starbursts and AGN with average L-H2O/L-FIR = -2.76(-1.21)(+1.21) x 10(-5). We find that the scatter in the observed L-H2O/L-FIR relation does not obviously correlate with the effective temperature of the dust spectral energy distribution or the molecular gas surface density. This is a first step in developing p-H2O(2(0,2) - 1(1,1)) as a resolved star formation rate calibrator.