The ATLAS Collaboration measures the inclusive production of Z bosons via their decays into electron and muon pairs in p + Pb collisions at root S-NN = 5.02 TeV at the Large Hadron Collider. The measurements are made using data corresponding to integrated luminosities of 29.4 and 28.1 nb(-1) for Z -> ee and Z -> mu mu, respectively. The results from the two channels are consistent and combined to obtain a cross section times the Z -> ll branching ratio, integrated over the rapidity region vertical bar y(Z)*vertical bar < 3.5, of 139.8 +/- 4.8 (statistical) +/- 6.2 (systematic) +/- 3.8 (luminosity) nb. Differential cross sections are presented as functions of the Z boson rapidity and transverse momentum and compared with models based on parton distributions both with and without nuclear corrections. The centrality dependence of Z boson production in p + Pb collisions is measured and analyzed within the framework of a standard Glauber model and the model's extension for fluctuations of the underlying nucleon-nucleon scattering cross section.