The tail of replication-dependent histone H3.1 varies from that of replication-independent H3.3 at the amino acid located at position 31 in plants and animals, but no function has been assigned to this residue to demonstrate a unique and conserved role for H3.1 during replication. We found that TONSOKU (TSK/TONSL), which rescues broken replication forks, specifically interacts with H3.1 via recognition of alanine 31 by its tetratricopeptide repeat domain. Our results indicate that genomic instability in the absence of ATXR5/ATXR6-catalyzed histone H3 lysine 27 monomethylation in plants depends on H3.1, TSK, and DNA polymerase theta (Pol θ). This work reveals an H3.1-specific function during replication and a common strategy used in multicellular eukaryotes for regulating post-replicative chromatin maturation and TSK, which relies on histone monomethyltransferases and reading of the H3.1 variant.