Background: The use of homologous recombination to precisely modify plant genomes has been challenging, due to the lack of efficient methods for delivering DNA repair templates to plant cells. Even with the advent of sequence-specific nucleases, which stimulate homologous recombination at predefined genomic sites by creating targeted DNA double-strand breaks, there are only a handful of studies that report precise editing of endogenous genes in crop plants. More efficient methods are needed to modify plant genomes through homologous recombination, ideally without randomly integrating foreign DNA. Results: Here, we use geminivirus replicons to create heritable modifications to the tomato genome at frequencies tenfold higher than traditional methods of DNA delivery (i.e., Agrobacterium). A strong promoter was inserted upstream of a gene controlling anthocyanin biosynthesis, resulting in overexpression and ectopic accumulation of pigments in tomato tissues. More than two-thirds of the insertions were precise, and had no unanticipated sequence modifications. Both TALENs and CRISPR/Cas9 achieved gene targeting at similar efficiencies. Further, the targeted modification was transmitted to progeny in a Mendelian fashion. Even though donor molecules were replicated in the vectors, no evidence was found of persistent extra-chromosomal replicons or off-target integration of T-DNA or replicon sequences. Conclusions: High-frequency, precise modification of the tomato genome was achieved using geminivirus replicons, suggesting that these vectors can overcome the efficiency barrier that has made gene targeting in plants challenging. This work provides a foundation for efficient genome editing of crop genomes without the random integration of foreign DNA.