The carbon capture-transportation-utilization (C-CTU) chain strengthens the coupling between terminal energy consumption and renewable energy resources (RES), achieving carbon emission reduction in power generation sectors. However, the dynamic operation of the C-CTU chain and the uncertainties induced by RES output pose new challenges for the low-carbon operation. To address above challenges, the nonlinear dynamic operation model of C-CTU chain is first proposed in this study. It is further incorporated into the day-ahead operation scheme of the electricity-carbon integrated system considering the stochastic nature of wind power. This scheme is treated as a two-stage stochastic integer programming (TS-SIP) problem with a mixed-integer nonlinear recourse. By means of the polyhedral envelope-based linearization method, this recourse is reformulated into its linear counterpart. To further improve the computational performance of classical decomposition algorithms, a novel Benders decomposition framework with hybrid cutting plane strategies is proposed to obtain better feasible solutions within a limited time. Simulations are conducted on two power system test cases with the C-CTU chain. Numerical results indicate that the engagement of C-CTU chain promotes the low-carbon economic operation of the power system. Also, the proposed decomposition algorithm shows a superior solution capability to handle large-scale TS-SIP than state-of-the-art commercial solvers.