Powertrain electrification incorporating advanced combustion-based dedicated hybrid engines (DHEs) is an effective and affordable approach to automotive energy saving. To explore the concealed fuel-saving potential of connected plug-in hybrid electric vehicles (CPHEVs) and manage engine dynamics, a data-driven predictive energy consumption minimization strategy (D-PECMS) is proposed in a hierarchical framework. The strategy relies on multi-source trip information provided by advanced driving assistance systems (ADAS) combined with maps and realizes power demand prediction by designing a multivariable long-term and short-term memory (M-LSTM) network. The upper level adopts dynamic programming (DP) to realize SOC planning, while the bottom layer utilizes D-PECMS to achieve computationally-efficient energy management with the engine combustion process being regulated in transient. This strategy is featured with predictive SOC tracking ability with less computational burden and look-ahead engine start-stop control. To ensure the credibility of validation, bench test data are used from a high-efficiency spark-induced compression ignition (SICI) engine to model the CPHEV, and the real-world driving scenarios are reconstructed based on real-time traffic data collected in China. The proposed D-PECMS strategy is tested through comprehensive experiments and compared against both the adaptive ECMS and offline DP. The results demonstrate that the proposed strategy effectively reduces fuel consumption by 3.1% and 13.2% in contrast to the adaptive ECMS and rule-based control respectively. Moreover, the D-PECMS strategy successfully avoids frequent engine operation mode switching as well as engine startup and shutdown.