In the present article, copper(I) complexes of bis(pyrazol-1-yl) carboxylic acid (LH), bis(3,5-dimethylpyrazol-1-yl) carboxylic acid (L2H), and bis(pyrazol-1-yl) acetates conjugated with an N-methyl-d-aspartate (NMDA) receptor antagonist (LNMDA or L2NMDA) and phosphane ligands (triphenylphosphine or 1,3,5-triaza-7-phosphaadamantane) were synthesized. The selection of an NMDA antagonist for the coupling with LH and L2H was suggested by the observation that NMDA receptors are expressed and play a role in different types of cancer models. All the new complexes showed a significant antitumor activity on a panel of human tumor cell lines of different histology, with cisplatin-sensitive, cisplatin-resistant, or multi-drug-resistant phenotype. Their half maximal inhibitory concentration (IC50) values were in the low- and sub-micromolar range and, in general, significantly lower than that of cisplatin. Interestingly, the fact that all the complexes proved to be significantly more active than cisplatin even in three-dimensional (3D) spheroids of H157 and BxPC3 cancer cells increased the relevance of the in vitro results. Finally, morphological analysis revealed that the most representative complex 8 induced a massive swelling of the endoplasmic reticulum (ER) membrane, which is a clear sign of ER stress.