The production cross sections of the B+, B0, and Bs0 mesons, and of their charge conjugates, are measured via exclusive hadronic decays in p+Pb collisions at the center-of-mass energy sNN=5.02  TeV with the CMS detector at the CERN LHC. The data set used for this analysis corresponds to an integrated luminosity of 34.6  nb-1. The production cross sections are measured in the transverse momentum range between 10 and 60  GeV/c. No significant modification is observed compared to proton-proton perturbative QCD calculations scaled by the number of incoherent nucleon-nucleon collisions. These results provide a baseline for the study of in-medium b quark energy loss in Pb+Pb collisions.