DNA molecules can be adopted to design biomolecular control circuits that can effectively control biochemical reaction processes. However, the leak reaction in actual biochemical reactions causes a significant uncertainty for reactions. In this paper, the first-order time-delay system is selected as the controlled object. A two-degree-of-freedom internal model PID controller (2DOF IMC-PID) is constructed for the first time within the framework of chemical reaction networks (CRNs). Under this control strategy, the set-point tracking and disturbance suppression are tuned with individual controllers, respectively. The controller parameters are determined by two filtering parameters that affect the controller’s performance, so the parameter tuning is simpler and more targeted. Then, the 2DOF IMC-PID controller is implemented in DSD reaction networks, with less overshoot in the 2DOF IMC-PID control system than the traditional PID control system and the 2DOF PID control system. Finally, a 2DOF IMC-PID division gate control system is established to effectively inhibit the impacts of leak reactions on the computation results. Although the leak reaction occurs at the division gate, the ideal output can be produced by the 2DOF IMC-PID division gate control system.