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 policy backfire by promoting their diffusion before electricity is decarbonised? 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 assessment. 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 global transport and heating demand. Even if future end-use electrification is not matched by rapid power sector decarbonisation, it likely avoids emissions in almost all world regions.