Glass-forming liquids grow dramatically sluggish upon cooling. This slowdown has long been thought to be accompanied by a growing correlation length. Characteristic dynamical and static length scales, however, have been observed to grow at different rates, which perplexes the relationship between the two and with the slowdown. Here, we show the existence of a direct link between local dynamical sluggishness and the extent of amorphous order, as captured by static point-to-set correlations. This link, which is stronger and more general than that observed with locally preferred structures, suggests a universal relationship between structure and dynamics in glass-forming liquids.