Molecular evolutionary rates vary among lineages and influence the evolutionary process. Here, we report elevated genome-wide mutation rates in Podostemaceae, a family of aquatic plants with a unique body plan that allows members to live on submerged rocks in fast-flowing rivers. Molecular evolutionary analyses using 1,640 orthologous gene groups revealed two historical increases in evolutionary rates: the first at the emergence of the family and the second at the emergence of Podostemoideae, which is the most diversified subfamily. In both branches, synonymous substitution rates were elevated, indicating higher mutation rates. On early branches, mutations were biased in favour of AT content, which is consistent with a role for ultraviolet light-induced mutation and a habitat shift. In ancestors of Podostemoideae, DNA-repair genes were enriched in genes under positive selection, which may have responded to the meristem architectural changes.