A new Cd-based coordination polymer (CP), [Cd2(L)2(PDA)2(H2O)2]·10H2O (where PDA = 1,4-phenylenediacetate and L = 2,4,5-tri-4-pyridyl-1H-imidazole), 1, was successfully synthesized by utilizing the layer diffusion method. Comprehensive characterization of 1 was conducted employing single-crystal X-ray diffraction, powder X-ray diffraction, thermogravimetric analysis, and Fourier transform infrared spectroscopy. Single-crystal X-ray diffraction revealed a three-dimensional supramolecular structure that originated from connectivity between the pentagonal bipyramidal coordination of Cd2+ ions and the two ligands (PDA and L) and water molecules. Compound 1 displayed significant photoluminescence-based sensing capabilities toward sulfonamide-containing antibiotics such as sulfamethazine (SMZ), sulfaquinoxaline (SQX), sulfadiazine (SDZ), sulfachloropyridazine (SCP), sulfameter (SM), sulfamethoxazole (SMX), and sulfathiazole (STZ) in an aqueous medium through the luminescence enhancement phenomena. Additionally, 1 demonstrated luminescence turn-off of the luminescence intensity in the presence of 2,4,6-trinitrophenol (TNP). The calculated limit of detection in an aqueous medium was 2.01 μM for sulfamethazine (SMZ) and 2.21 μM for TNP. The differential luminescence responses in the presence of electron-rich antibiotics and electron-deficient TNP were corroborated using the density functional theory. The application of compound 1 as a catalyst in the Knoevenagel reaction yielded an appreciable outcome, and it showed decent catalytic efficiency toward the Knoevenagel reaction between malononitrile and various aromatic aldehydes at room temperature by utilizing the free basic sites (pyridine moieties).