A series of silver(I) complexes with semirigid di-2-pyrimidyl sulfide (DprS), namely, {[Ag2(DprS)2(CF3CO2)](CF3CO2)·2H2O}∞ (1), {[Ag6(DprS)6(CF3SO3)5](CF3SO3)·3.5H2O}∞ (2), {[Ag2(DprS)(C2F5CO2)2]}∞ (3), [Ag(DprS)(NO3)∞ (4), and {[Ag3(DprS)3](ClO4)3}∞ (5), have been synthesized and characterized by single-crystal X-ray analysis. The silver(I) complexes 1–2 and 4–5 exhibit one-dimensional tape-like coordination polymers with different topological structures, while complex 3 has a two-dimensional coordination network. In these complexes, the two pyrimidyl rings of each DprS are almost in an orthogonal orientation, a rigid nonplanar conformation, and the multidentate ligand adopts an unvaried N,N′,N″-μ3 ligation mode despite the different anions (CH3COO– in 1, CF3SO3– in 2, C2F5COO– in 3, NO3– in 4, and ClO4– in 5). Attractive intramolecular Npyrimidyl···Cpyrimidyl interaction between a 1-positional N atom of one pyrimidyl ring and an electrophilic 2-positional C atom of the other ring of DprS is a common dominant interaction, which drives and stabilizes the nonplanar ligand conformation in these crystalline structures. Calculation through the self-consistent field crystal orbital method based on density functional theory indicates the presence of the N···C contact, a nucleophile–electrophile affinity. Unconventional anion−πpyrimidyl interactions engaged in the construction of the supramolecular architectures of 1–5 also are presented and discussed.