The paper proposes a power-split Hybrid Electric Vehicle (HEV) control strategy that combines a rule-based (RB) controller, including State-of-Charge (SoC) controller and engine start/stop logic, with a precisely formulated equivalent consumption minimisation strategy (ECMS). An 1D and 2D directional search-based instantaneous ECMS optimisation is used to find optimal power train points in high-efficiency engine map regions that are previously determined by an off-line optimisation approach. The simulation results confirm that the RB controller performance can be significantly improved when extended with the proposed ECMS formulation, without requiring an adaptive empirical penalty factor to satisfy the SoC sustainability condition. The proposed RB+ECMS control strategies have been verified against dynamic programming-based optimisation benchmark for different certification driving cycles.