Two new families of dithiocarbamate gold(I) complexes derived from benzenesulfonamide with phosphine or carbene as ancillary ligands have been synthesized and characterized. In the screening of their in vitro activity on human colon carcinoma cells (Caco-2), we found that the more lipophilic complexes—those with the phosphine PPh3—exhibited the highest anticancer activity whilst also displaying significant cancer cell selectivity. [Au(S2CNHSO2C6H5)(PPh3)] (1) and [Au(S2CNHSO2-p-Me-C6H4)(IMePropargyl)] (8) produce cell death, probably by intrinsic apoptosis (mitochondrial membrane potential modification) and caspase 3 activation, causing cell cycle arrest in the G1 phase with p53 activation. Besides this, both complexes might act as multi-target anticancer drugs, as they inhibit the activity of the enzymes thioredoxin reductase (TrxR) and carbonic anhydrase (CA IX) with the alteration of the redox balance, and show a pro-oxidant effect.