Conventional economic growth models treat production/consumption as abstractions linked only by money flows, disregarding their connection to the physical world. Nevertheless, the existing literature suggests that energy flows can influence production and links useful exergy prices with economic growth. Useful exergy is energy measured at the stage where it produces an end-use (and is a measurement of energy quality). Not all approaches in the literature use this metric and they often consider energy as a primary input (despite it being an intermediate input). We explore the relationship between energy flows and economic growth for the US through a framework where useful exergy, the output of an “extended energy sector” (where all effects of increasing primary-to-final-to-useful exergy efficiency are located), is an intermediate input for a “non-energy sector”. Together, they encompass the entire economy. We conclude that the share of investment in the extended energy sector grew with the overall economic growth throughout 1960–2020, while the labour share decreased. The non-energy sector contributed the largest share of consumption, exports, imports and labour. In recent years, the energy sector has overtaken it in terms of investment. Our two-sector model has important implications for current climate policy, namely regarding the Integrated Assessment Models on which it is based.