A newly arisen Y-chromosome can become established in one part of a species range by genetic drift or through the effects of selection on sexually antagonistic alleles. However, it is difficult to explain why it should then spread throughout the species range after this initial episode. As it spreads into new populations, it will actually enter females. It would then be expected to perform poorly since it will have been shaped by the selective regime of the male-only environment from which it came. We address this problem using computer models of hybrid zone dynamics where a neo-XY chromosomal race meets the ancestral karyotype. Our models consider that the neo-Y was established by the fusion of an autosome with the ancestral X-chromosome (thereby creating the Y and the 'fused X'). Our principal finding is that sexually antagonistic effects of the Y induce indirect selection in favour of the fused X-chromosomes, causing their spread. The Y-chromosome can then spread, protected behind the advancing shield of the fused X distribution. This mode of spread provides a robust explanation of how newly arisen Y-chromosomes can spread. A Y-chromosome would be expected to accumulate mutations that would cause it to be selected against when it is a rare newly arrived migrant. The Y can spread, nevertheless, because of the indirect selection induced by gene flow (which can only be observed in models comprising multiple populations). These results suggest a fundamental re-evaluation of sex-chromosome hybrid zones. The well-understood evolutionary events that initiate the Y-chromosome's degeneration will actually fuel its range expansion.