The growing interest in hybrid (aqueous–organic) electrolytes for electrochemical energy storage is due to their wide stability window, improved safety, and ease of assembly that does not require a moisture-free atmosphere. When it comes to applications in electrochemical capacitors, hybrid electrolytes are expected to fill the gap between high-voltage organic systems and their high discharge rate aqueous counterparts. This article discusses the potential applicability of aqueous–organic electrolytes utilizing water/N,N-dimethylacetamide (DMAc) solvent mixture, and sodium perchlorate as a source of charge carriers. The hydrogen bond formation between H2O and DMAc (mole fraction xDMAc = 0.16) is shown to regulate the original water and cation solvation structure, thus reducing the electrochemical activity of the primary aqueous solution both in the hydrogen (HER) and oxygen (OER) evolution reactions region. As a result, an electrochemical stability window of 3.0 V can be achieved on titanium electrodes while providing reasonable ionic conductivity of 39 mS cm−1 along with the electrolyte’s flame retardant and anti-freezing properties. Based on the diagnostic electrochemical studies, the operation conditions for carbon/carbon capacitors have been carefully optimized to adjust the potential ranges of the individual electrodes to the electrochemical stability region. The system with the appropriate electrode mass ratio (m+/m− = 1.51) was characterized by a wide operating voltage of 2.0 V, gravimetric energy of 13.2 Wh kg−1, and practically a 100% capacitance retention after 10,000 charge–discharge cycles. This translates to a significant rise in the maximum energy of 76% when compared to the aqueous counterpart. Additionally, reasonable charge–discharge rates and anti-freeze properties of the developed electrolyte enable application in a broad temperature range down to −20 °C, which is demonstrated as well.