Bis(pyrazol-1-yl)acetic acid (HC(pz)2COOH) and bis(3,5-dimethyl-pyrazol-1-yl)acetic acid (HC(pzMe2)2COOH) were converted into the methyl ester derivatives 1 (LOMe) and 2 (L2OMe), respectively, and were used for the preparation of silver(I) complexes 3–5. The Ag(I) complexes were prepared by the reaction of AgNO3 and 1,3,5-triaza-7-phosphaadamantane (PTA) or triphenylphosphine (PPh3) with LOMe and L2OMe in methanol solution. All Ag(I) complexes showed a significant in vitro antitumor activity, proving to be more effective than the reference drug cisplatin in the in-house human cancer cell line panel containing examples of different solid tumors. Compounds were particularly effective against the highly aggressive and intrinsically resistant human small-cell lung carcinoma (SCLC) cells, either in 2D and 3D cancer cell models. Mechanistic studies revealed their ability to accumulate into cancer cells and to selectively target Thioredoxin (TrxR), thus leading to redox homeostasis unbalance and ultimately inducing cancer cell death through apoptosis.