Tetrahedral copper(I) TpCuP complexes 1-15, where Tp is a N,N,N-tris(azolyl)borate and P is a tertiary phosphine, have been synthesized and characterized by means of NMR, ESI-MS, and XAS-EXAFS, and X-ray diffraction analyses on the representative complexes 1 and 10, respectively. All copper(I) complexes were evaluated for their antiproliferative activity against a panel of human cancer cell lines (including cisplatin and multidrug-resistant sublines). The two most effective complexes [HB(pz)3]Cu(PCN), 1, and [HB(pz)3]Cu(PTA), 2, showed selectivity toward tumor vs normal cells, inhibition of 26S proteasome activity associated with endoplasmic reticulum (ER) stress, and unfolded protein response (UPR) activation. No biochemical hallmarks of apoptosis were detected, and morphology studies revealed an extensive cytoplasmic vacuolization coherently with a paraptosis-like cell death mechanism. Finally, the antitumor efficacy of complex 1 was validated in the murine Lewis Lung Carcinoma (LLC) model.