In the United States, burning coal at power plants results in a little more than 40% of all mercury emissions from man-made sources (Source: Section 2.7 of the 2014 National Emissions Inventory, version 1 (December 2016) of the Technical Support Document (PDF)). While LED bulbs are more efficient, last longer, and are more versatile than either CFLs or incandescent bulbs, using energy-saving CFLs instead of incandescent bulbs reduces demand for electricity, which in turn reduces the amount of coal burned by power plants, which reduces emissions of mercury when the coal is burned.
A 13-watt, 8,000-rated-hour-life CFL (60-watt equivalent; a common light bulb type) will save 376 kWh over its lifetime, thus avoiding 4.3 mg of mercury. If the bulb goes to a landfill, overall emissions savings would drop a little, to 3.9 mg. EPA recommends that CFLs are recycled where possible, to maximize mercury savings.