Gas has become the main fuel for electricity production as a result of the significant growth in gas‐fired units (GFU), which can lead to a shortage of supply gas for power generation. Meanwhile, there is a higher chance of power mismatch due to the rising penetration of renewable energy in the power system. Considering that power system and gas natural network are increasingly interdependent under more coupling elements, such as power‐to‐gas (PtG) and GFU, cascading failures will occur more often if demand mismatch is not dealt with efficiently. To explore the potential of PtG and GFU to enhance the flexibility of the integrated power and gas system (IPGS), the collaborative load shifting effect (LSE) of them is researched. Therefore, this article contributes a two‐stage robust energy scheduling model that considers the LSE of PtG and GFU on the electric and gas demand side. Simplifying the dual process in the max–min optimization, this article applies a modified Benders decomposition methodology introducing virtual balance to solve the model. Also, the LSE of PtG and GFU is demonstrated in the form of security region (SR) in the case study. Based on the proposed load uniformity level (LUL) index, the results show that GFU and PtG are mainly involved in the load shifting in the power system, and PtG prefers to work when load shifting level is high. As a result, the equipment of PtG and GFU increases the SR by 40.9% and 14.3%, respectively. Moreover, the impact of the fluctuation of wind power on the IPGS, especially on the natural gas network (NGN), is validated through the reduction of the load shifting range by 5%.