Storm events have a notable impact on natural organic matter (NOM) and trihalomethanes (THMs). Water samples were collected and analyzed from Ulutan Dam (UD), in the Zonguldak region, Turkey. During four storm events, the data indicated the presence of hysteresis patterns in three of the four storms, with elevated concentrations of organic constituents observed during the falling limb of the hydrographs. It was observed that a higher specific THM (sp.THM) concentration (201.83 µg/L) was reached with an average specific UV absorbance (SUVA) value of 6.66 L/mg·m in the fourth storm. This means that the primary sources of THM precursors are the aromatic compounds present in NOM. A significant correlation between UV absorbance (UV254) and dissolved organic carbon (DOC) (R = 0.99–0.92) for all storms was observed. Chlorine demand also yielded a strong correlation (R = 0.81–0.99) with UV254 and DOC. Therefore, the present study indicates that UV254 can be an effective parameter for monitoring applicable chlorine dosage in drinking water treatment management as faced with storm events. On the other hand, the results of the study also provide valuable insight into the direct and indirect link between short-term precipitation events and their impact on the structural and THM precursors in surface water sources.