We present a calculation of direct photon production at next-to-leading order of QCD and a matching of this calculation with parton showers using POWHEG BOX. Based on simulations with POWHEG+PYTHIA, we perform a detailed phenomenological analysis of PHENIX data on prompt photon production and photon-hadron jet correlations in pp collisions at RHIC, considerably improving the description of these data with respect to previous calculations, and we suggest additional interesting analyses.