The wide application of energy conversion facilities on the demand side, such as combined heat and power units, has accelerated the integration of multiple energy carriers in the form of Energy Hub (EH). EH can flexibly schedule its electricity and gas consumption patterns to provide demand response (DR) services to the electricity system. However, DR can introduce significant uncertainties in gas demands, posing challenges to the real-time balance of the integrated electricity and gas systems (IEGS). The gas stored in the pipeline (i.e., linepack) is a promising flexible resource to accommodate the gas demand uncertainties during the DR. However, using linepack is challenging due to the complex physical characteristics of gas flow dynamics. This paper proposes a coordinated optimal control framework for both EH and IEGS, focusing on leveraging the linepack flexibility to enhance DR capabilities. Firstly, a multi-level self-scheduling framework for the EH is developed to comprehensively explore the DR potential. The gas flow dynamic constraints are then formulated to ensure that the fluctuating gas demand can be accommodated by the linepack in the IEGS. The second-order cone (SOC) relaxation is adopted to convexify the nonlinearity in the motion equation of gas flow dynamics. To tackle the overall mixed-integer SOC programming problem, an enhanced Benders decomposition strategy that incorporates the lift-and-project cutting plane method is developed, along with a novel solution procedure. The proposed method is validated using the IEEE 24-bus Reliability Test System and the Belgium natural gas transmission system to demonstrate its effectiveness.