Hybrid sterility maintains reproductive isolation between species by preventing them from exchanging genetic material. The genome sequences of the yeasts Saccharomyces paradoxus and Saccharomyces paradoxus have diverged by about 12%, yet they can mate and form viable diploid hybrids, which can reproduce asexually by mitosis. But these hybrids are sexually sterile: nearly all the gametes they produce by meiosis are inviable because they are aneuploid, lacking at least one essential chromosome. Chromosomes from the different species mis-segregate during hybrid meiosis due to anti-recombination; their sequences are too diverged to efficiently recombine and form crossovers. Previous methods to increase hybrid fertility by enhancing meiotic crossing over have had counteracting detrimental effects on asexual viability, due to increased mutagenesis and ectopic recombination. We were able to increase hybrid fertility 70-fold by suppressing two genes, MSH2 (YOL090W) and SGS1 (YMR190C), specifically during meiosis, whilst maintaining their mitotic expression. This confirms that anti-recombination is the principal cause of hybrid sterility. By overcoming this barrier, we were able to generate viable euploid hybrid gametes containing recombinant genomes from these two highly diverged parent species. We used this unique resource to map intrinsic Bateson-Dobzhansky-Muller incompatibilities contributing to hybrid gamete inviability. The ability to interbreed such diverged species will allow mapping of other intrinsic traits such as hybrid depression or vigour, extrinsic ecological adaptations that differentiate species, or commercially important characteristics.