The electrification of passenger road transport and household heating features prominently in current and planned policy frameworks to achieve greenhouse gas emissions reduction targets. However, since electricity generation involves using fossil fuels, it is not established where and when the replacement of fossil-fuel-based technologies by electric cars and heat pumps can effectively reduce overall emissions. Could electrification policies backfire by promoting their diffusion before electricity is decarbonized? Here we analyse current and future emissions trade-offs in 59 world regions with heterogeneous households, by combining forward-looking integrated assessment model simulations with bottom-up life-cycle assessments. We show that already under current carbon intensities of electricity generation, electric cars and heat pumps are less emission intensive than fossil-fuel-based alternatives in 53 world regions, representing 95% of the global transport and heating demand. Even if future end-use electrification is not matched by rapid power-sector decarbonization, it will probably reduce emissions in almost all world regions.