Rising energy expenses, the shift towards renewable sources, and grid congestion considerably affect the operations of container terminals. To tackle these challenges, it is necessary to implement energy-aware integrated operational planning which considers related uncertainties. This work proposes a two-stage stochastic mixed integer programming model to optimize container terminal operations planning and demand-responsive energy management. To this end, energy consumption is shifted whenever operationally possible and economically beneficial. We solve the proposed model by developing a dedicated progressive hedging algorithm. Operations considered in this model include vessel scheduling at berths, temperature control of refrigerated containers, and allocation of handling capacity of quay cranes, yard cranes, and automated guided vehicles to serve each vessel. Various scenarios for vessel arrival times and electricity prices are explored representing the uncertainty of energy demand and supply, respectively, based on a case study of the Altenwerder container terminal in Hamburg. Our results suggest potential cost savings of 5.9 per cent on average with a single energy price based on a long-term contract and 13.2 per cent when applying varying real-time electricity prices based on wholesale market rates. These findings underscore the substantial potential of demand response strategies for (electrified) container terminal operations.