Exploring the economic value of carbon sinks in agricultural systems can improve the development of sustainable agriculture. However, there are few studies on the economic value of farmland carbon sinks from a systemic perspective. This study takes Zhejiang, China’s first common wealth demonstration zone, as an example, and quantifies the carbon sinks in farmland and their economic value. The driving mechanism is analyzed by using a system dynamics model. The potential value and management of farmland carbon sinks are discussed. The results show that from 2007 to 2021, the average annual carbon sinks in farmland of Zhejiang were 5.84 million tons, a downward trend. The annual economic value was CNY 149.80 million, a marked upward trend. A rational fertilization project is a win-win ecological and economical measure to enhance the carbon sinks in farmland. Artificially increasing the carbon price to 32% will help Zhejiang achieve the core goal of the common prosperity plan, bringing the urban–rural income gap below 1.9 in 2025. Achieving the economic value of farmland carbon sinks is a green way to narrow the urban–rural income gap. Our study indicates that the marketization of carbon sinks in agricultural land systems may be a very promising path to promote green agriculture.