Efficient energy supply is key to reduce industrial greenhouse gas emissions. In the industry, energy is often supplied by on-site utility systems with electricity grid connection. Usually, electricity from the grid is assumed to have annually averaged emission factors when greenhouse gas emissions are calculated. However, emissions from electricity production are in fact time-dependent to match continuously varying demand and supply. These time dependent emissions offer the potential to reduce emissions by temporal shifting of electricity demand in demand-side management. Here, we investigate the impact of time-dependent grid mix emissions for low-carbon utility systems. For this purpose, we present a detailed mixed-integer linear programming model for a low-carbon utility system. Subsequently, we compute time-dependent grid emission factors based on the current mix and based on the marginal technologies. These grid emission factors serve as input to determine and economic and environmental trade-off curves. We show that emissions can be reduced by up to 6% at the same costs by considering time-dependent grid mix emissions, instead of annual average grid emissions. Marginal time-dependent emission factors even allow to reduce emissions by up to 60%. Our work shows that time-dependent grid emissions factors could enable climate-friendly demand-side management leading to significant emission reductions.