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Increasing the fuel economy of hybrid electric vehicles (HEVs) and extended range electric vehicles (EREVs) through optimization-based energy management strategies (EMS) has been an active research area in transportation. However, it is difficult to apply optimization-based EMS to current in-use EREVs because insufficient knowledge is known about future trips, and because such methods are computationally expensive for large-scale deployment. As a result, most past research has been validated on standard driving cycles or on recorded high-resolution data from past real driving cycles. This paper improves an in-use rule-based EMS that is used in a delivery vehicle fleet equipped with two-way vehicle-to-cloud connectivity. A physics model-guided online Bayesian framework is described and validated on large number of in-use driving samples of EREVs used for last-mile package delivery. The framework includes: a database, a preprocessing module, a vehicle model and an online Bayesian algorithm module. It uses historical 0.2 Hz resolution trip data as input and outputs an updated parameter to the engine control logic on the vehicle to reduce fuel consumption on the next trip. The key contribution of this work is a framework that provides an immediate solution for fuel use reduction of in-use EREVs. The framework was also demonstrated on real-world EREVs delivery vehicles operating on actual routes. The results show an average of 12.8% fuel use reduction among tested vehicles for 155 real delivery trips. The presented framework is extendable to other EREV applications including passenger vehicles, transit buses, and other vocational vehicles whose trips are similar day-to-day.