The integration of large-scale renewable distributed generation (DG) units in distribution networks brings new challenges for real-time power dispatch, including active power and reactive power (P-Q) coupling and operational uncertainties. To reduce the conservativeness of robust optimization (RO) solutions, this paper proposes a distributionally robust real-time power dispatch model, which characterizes the uncertainty of DG output with the information of first-order and second-order moments. Furthermore, a two-stage scheme, which includes economic dispatch (ED) and corrective control, is incorporated in the model, in which ED optimizes the active power schedule and corrective control strategies of P-Q are generated to eliminate overvoltage problems. The proposed model can be transformed into an equivalent semidefinite programming problem and solved via the delayed constraint generation algorithm. Numerical test results show that the proposed model reduces operational costs and mitigates overvoltage problems significantly compared with the conventional one-stage model. The proposed model also outperforms the conventional RO model by exploiting probability information to achieve statistically optimal dispatch.