Pavement roughness affects rolling resistance and thus vehicle fuel consumption. When a vehicle travels at constant speed on an uneven road surface, the mechanical work dissipated in the vehicle’s suspension system is compensated by vehicle engine power and results in excess fuel consumption. This dissipation depends on both road roughness and vehicle dynamic characteristics. This paper proposes, calibrates, and implements a mechanistic model for roughness-induced dissipation. The distinguishing feature of the model is its combination of a thermodynamic quantity (energy dissipation) with results from random vibration theory to identify the governing parameters that drive the excess fuel consumption caused by pavement roughness, namely, the international roughness index (IRI) and the waviness number, w (a power spectral density parameter). It is shown through sensitivity analysis that the sensitivity of model output, that is, excess fuel consumption, to the waviness number is significant and comparable to that of IRI. Thus, introducing the waviness number as a second roughness index, in addition to IRI, allows a more accurate quantification of the impact of surface characteristics on vehicle fuel consumption and the corresponding greenhouse gas emissions. This aspect is illustrated by application of the roughness–fuel consumption model to two road profiles extracted from FHWA’s Long-Term Pavement Performance database.