Achieving an emission pathway that would be compatible with limiting the global temperature increase to 1.5 °C compared with pre-industrial levels would require unprecedented changes in the economy and energy use and supply. This paper describes how such a transition may impact the dynamics of sectoral emissions. We compare contrasted global scenarios in terms of the date of emission peaks, energy efficiency, availability of low-carbon energy technologies, and fossil fuels, using the global integrated assessment model IMACLIM-R. The results suggest that it is impossible to delay the peak of global emissions until 2030 while remaining on a path compatible with the 1.5 °C objective. We show that stringent policies in energy-demand sectors—industry and transportation especially—are needed in the short run to trigger an immediate peak of global emissions and increase the probability to meet the 1.5 °C objective. Such sector-specific policies would contribute to lowering energy demand and would reduce the level of the carbon price required to reach the same temperature objective. Bringing forward the peak of global emissions does not lead to a homothetic adjustment of all sectoral emission pathways: an early peak of global emissions implies the fast decarbonization of the electricity sector and early emission reductions in energy-demand sectors—mainly industry and transportation.