Traditional annular multiphase flow pressure models often assume constant drilling fluid flow rates and static gas influx rates when calculating bottomhole pressure, making it difficult to accurately capture transient wellbore processes. To address this limitation, this paper proposes a time-varying transient flow model that incorporates a dynamic coupling mechanism between drilling fluid flow and gas influx rates, enabling precise characterization of their real-time dynamic interactions within the wellbore. The model employs an explicit finite volume method for numerical solution, with experimental validation demonstrating a prediction accuracy of 92.7%. Key findings reveal that under dynamic gas influx conditions (0.3–0.6 kg/s), bottomhole pressure surges instantaneously by 4.1 MPa, while wellhead pressure peaks increase by 0.6 MPa. When drilling fluid flow rises to 23.68 kg/s, bottomhole and wellhead pressures increase by 1.1 MPa and 0.16 MPa, respectively. Notably, high-flow conditions (>23 kg/s) enhance cuttings transport efficiency but suppress gas expansion due to significantly increased frictional pressure losses. The model clearly elucidates the dynamic coupling mechanism between drilling fluid flow and gas influx rates and its critical impact on wellbore pressure, establishing a fundamental theoretical basis for optimizing drilling fluid flow control during gas influx events and significantly reducing well control risks.