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