The key challenge created by global climate change is to implement effective carbon–neutral programs. The carbon sequestration service (CSS) establishes spatial and temporal connections between carbon sequestration supply and demand, so accurate scientific quantification of the CSS supply–demand balance is essential. However, a standard assessment framework for quantifying CSS supply–demand is currently lacking. In this study, we developed a spatio-temporal assessment framework for quantifying CSS supply–demand balance under land use change, based on the SPANs model. We followed the flow of CSS from supply to demand areas through spatial visualization based on the main wind direction and defined the transport path and quantity of CSS flow, taking Lancang Mekong River Basin (LMRB) as a case. The results showed that: (1) The total supply of CSS decreased by 1.14 million tons from 2000 to 2020, and total demand for CSS increased by 8.1 million tons. (2) CSS surplus areas were mainly concentrated in forested regions, with a maximum surplus of 4.31 t/ha. Deficit areas were dominated by cultivated land and artificial surfaces, with a maximum deficit of −1101.21 t/ha. There was spatial heterogeneity in CSS distribution and a clear imbalance between supply and demand. (3) Three out of six countries in the basin showed significant changes in CSS flow, with a decrease in demand area observed in Thailand and an increase in demand area observed in Cambodia and Vietnam. (4) CSS flow was mainly from north to south, with higher CSS in Thailand and lower flow in China. Thus the analysis revealed supply–demand imbalances in CSS and provided an objective understanding of the spatial flow of CSS. This scientific and intuitive theoretical basis and data support can be used for regional carbon management in LMRB and global carbon balance control.