To address the problems of large backflow power and reduced transmission efficiency of the neutral-point-clamped hybrid three-level dual-active-bridge converter (NPCH3L-DAB) operating over a wide power range, a backflow-power minimization control strategy based on triple-phase-shift (TPS) modulation and Karush-Kuhn-Tucker (KKT) optimality conditions is proposed. First, considering the three-level topology, the transmission power characteristics, current stress, and backflow power mechanism of the converter under two operating states with TPS modulation are analyzed. The analytical expressions of the inductor current, transmission power, and backflow power are derived. Second, with backflow power minimization as the objective and soft-switching operation as the constraint, a Lagrange-multiplier-based optimization model is established. The optimal phase-shift combinations for the two operating modes are obtained through the KKT conditions, thereby effectively suppressing the backflow power of the NPCH3L-DAB converter while ensuring zero-voltage switching of the power switches. Finally, a simulation model and an experimental platform are built to compare the proposed strategy with conventional single-phase-shift control and advanced modulation strategies. The results show that the proposed TPS-based optimal control strategy can effectively reduce backflow power over a wide power range, especially in the low- and medium-power regions. Under load transient conditions, the output voltage recovers smoothly and the system exhibits a fast dynamic response. Compared with conventional single-phase-shift control, the proposed strategy improves transmission efficiency under both low- and high-power operating conditions, with a maximum efficiency improvement of approximately 22% in the low-power mode. Moreover, under a similar voltage conversion ratio, the proposed strategy achieves better backflow power suppression in the medium- and low-power ranges than the existing unified optimal modulation strategy. Simulation and experimental results verify the effectiveness and feasibility of the proposed control method in reducing backflow power, improving transmission efficiency, and achieving soft switching.