Decarbonizing the energy system by electrification of heat and transport is only effective when using low-carbon electricity sources. As many countries such as Switzerland rely on imported electricity to meet their demand, the greenhouse gas (GHG) content of electricity imports must be correctly accounted for. By assuming an average GHG content for each amount imported, impacts of electricity required in peak periods are underestimated because this additional (marginal) demand is primarily met with fossil power plants. This study employs a model to capture marginal GHG contents of imported electricity from a direct and indirect (life-cycle) perspective at an hourly resolution. Implications on GHG are explored for various electricity demand and supply scenarios including electrification of heat and transport, large-scale expansion of renewables, and nuclear phase-out. We find that depending on the scenario, the average GHG intensity of consumed electricity may double, while diurnal and seasonal variations are even larger. Nonetheless, results show substantial GHG mitigation up to 45% with electrification in case of deploying a diversified electricity generation portfolio including photovoltaics and wind. For optimal GHG mitigation, short-term flexibility as provided by hydropower is necessary to manage electricity surpluses. The main challenge, however, surrounds seasonal energy storage including sector coupling.