Why sexual reproduction has evolved to be such a widespread mode of reproduction remains a major question in evolutionary biology. Although previous studies have shown that increased sex and recombination can evolve in the presence of host–parasite interactions (the ‘Red Queen hypothesis’ for sex), many of these studies have assumed that multiple loci mediate infection vs. resistance. Data suggest, however, that a major locus is typically involved in antigen presentation and recognition. Here, we explore a model where only one locus mediates host–parasite interactions, but a second locus is subject to directional selection. Even though the effects of these genes on fitness are independent, we show that increased rates of sex and recombination are favoured at a modifier gene that alters the rate of genetic mixing. This result occurs because of selective interference in finite populations (the ‘Hill–Robertson effect’), which also favours sex. These results suggest that the Red Queen hypothesis may help to explain the evolution of sex by contributing a form of persistent selection, which interferes with directional selection at other loci and thereby favours sex and recombination.