Most spontaneous DNA double-strand breaks (DSBs) result from replication-fork breakage. Break-induced replication (BIR), a genome rearrangement-prone repair mechanism that requires the Pol32/POLD3 subunit of eukaryotic DNA Pol delta, was proposed to repair broken forks, but how genome destabilization is avoided was unknown. We show that broken fork repair initially uses error-prone Pol32-dependent synthesis, but that mutagenic synthesis is limited to within a few kilobases from the break by Mus81 endonuclease and a converging fork. Mus81 suppresses template switches between both homologous sequences and diverged human Alu repetitive elements, highlighting its importance for stability of highly repetitive genomes. We propose that lack of a timely converging fork or Mus81 may propel genome instability observed in cancer.