New species arise from pre-existing species and inherit similar genomes and environments. This predicts greater similarity of the tempo of molecular evolution between direct ancestors and descendants, resulting in autocorrelation of evolutionary rates in the tree of life. Surprisingly, molecular sequence data have not confirmed this expectation, possibly because available methods lack the power to detect autocorrelated rates. Here, we present a machine learning method, CorrTest, to detect the presence of rate autocorrelation in large phylogenies. CorrTest is computationally efficient and performs better than the available state-of-the-art method. Application of CorrTest reveals extensive rate autocorrelation in DNA and amino acid sequence evolution of mammals, birds, insects, metazoans, plants, fungi, parasitic protozoans, and prokaryotes. Therefore, rate autocorrelation is a common phenomenon throughout the tree of life. These findings suggest concordance between molecular and nonmolecular evolutionary patterns, and they will foster unbiased and precise dating of the tree of life.