Understanding carbon emission profile of cities from multiple perspectives is a prerequisite to design just and effective carbon reduction policies. Previous studies on CO2 emissions by cities are usually confined to production or consumption-based perspective, while income-based perspective has been neglected. To fill the gap, direct emissions (a.k.a. production-based emissions), upstream emissions driven by final demand (a.k.a. consumption-based emissions) and downstream emissions enabled by primary input (a.k.a. income-based emissions) in an urban economy are comprehensively explored and compared for the first time, taking Beijing as a case. In the period of 2005-2012, Manufacture of Nonmetallic Mineral Products/Construction/Processing of Petroleum, Coking, Processing of Nuclear Fuel is identified as the key contributor to carbon emission by Beijing from the production/consumption/income-based perspective, respectively, indicating each perspective can unveil important information which the other methods fail to discover. Moreover, driving forces of CO2 emissions change in Beijing are uncovered using the structural decomposition analysis (SDA) from both the demand and supply sides. Emission intensity, production input and output structure change contribute to CO2 emission decrease in Beijing, which are largely offset by population, final demand/primary input level and final demand/primary input structure change, resulting in a net 3.9 Mt reduction during 2005-2012. While current policies continue to highlight end-of-pipe measures in cities, more attention should be paid to demand (e.g., encouraging low-carbon consumption) and supply side (e.g., controlling capital investment in enterprises with large income-based CO2 emissions).