Distribution optimal power flow (D-OPF) with peak load shaving function is crucial for guaranteeing economical and reliable operations of active distribution grids with various distributed energy resources. However, conventional D-OPF methods reduce only the power operation cost without considering carbon emission reduction, which may lead to a slowdown in achieving global carbon neutrality. To resolve this issue, this study proposes a deep reinforcement learning (DRL)-assisted D-OPF framework realizing dual-peak shaving of power and carbon emission for low-carbon active distribution system operations based on the notion of carbon emission flow (CEF). The proposed framework aims to minimize the total power operation costs of substation and gas-turbine (GT) generators. It also aims to reduce the total carbon emission cost via mitigation of peak power and carbon emission in the CEF-based D-OPF framework with both power and carbon emission peak constraints. A key feature of the proposed framework is the adoption of the DRL method for the CEF-based D-OPF problem to determine economical and eco-friendly peaks of power and carbon emission under dynamically changing distribution system operations. Furthermore, a D-OPF optimization-based reward function for the DRL agent is designed to yield no constraint violations for the D-OPF problem during the agent’s training phase. Numerical examples conducted on the IEEE 33-node and IEEE 69-node distribution systems with GT generators, solar photovoltaic systems, and energy storage systems demonstrate that, in contrast with CEF-free and CEF-integrated optimization methods with fixed power and/or carbon emission peaks, the proposed method further reduces the total carbon emission and cost.