If protein evolution is due in large part to slightly deleterious amino acid substitutions, then the rate of evolution should be greater in proteins that contribute less to individual fitness. The rationale for this prediction is that relatively dispensable proteins should be subject to weaker purifying selection, and should therefore accumulate mildly deleterious substitutions more rapidly. Although this argument was presented over twenty years ago, and is fundamental to many applications of evolutionary theory, the prediction has proved difficult to confirm. In fact, a recent study showed that essential mouse genes do not evolve more slowly than non-essential ones. Thus, although a variety of factors influencing the rate of protein evolution have been supported by extensive sequence analysis, the relationship between protein dispensability and evolutionary rate has remained unconfirmed. Here we use the results from a highly parallel growth assay of single gene deletions in yeast to assess protein dispensability, which we relate to evolutionary rate estimates that are based on comparisons of sequences drawn from twenty-one fully annotated genomes. Our analysis reveals a highly significant relationship between protein dispensability and evolutionary rate, and explains why this relationship is not detectable by categorical comparison of essential versus non-essential proteins. The relationship is highly conserved, so that protein dispensability in yeast is also predictive of evolutionary rate in a nematode worm.