Marginal CO₂ abatement cost curves derived from bottom-up or top-down models are widely used by policymakers to determine the least-cost sequential order of decarbonization measures and the most effective decarbonization strategies. However, most model-based methods lack high temporal, sectoral, and techno-economic resolution. To address these limitations, this paper presents a linear optimization method with an hourly resolution for a sector-coupled power system to derive step-wise CO₂ abatement cost curves. A step-wise marginal CO₂ abatement cost curve is calculated based on hundreds of hourly dispatch model runs, giving a high level of detail on techno-economic, inter-temporal, and inter-sectoral interactions. Results demonstrate a dynamic relationship between technology-specific CO₂ abatement costs, CO₂ emission reductions, and total system cost development per installed decarbonization measure. Moreover, the results indicate how competing flexibility and decarbonization options interact and how least-cost decarbonization pathways can be reached.