The evolution of sex is one of the greatest mysteries in evolutionary biology. An even greater mystery is the evolution of obligate sex, particularly when competing with facultative sex and not with complete asexuality. Here, we develop a stochastic simulation of an obligate allele invading a facultative population, where males are subject to sexual selection. We identify a range of parameters where sexual selection can contribute to the evolution of obligate sex: Especially when the cost of sex is low, mutation rate is high, and the facultative individuals do not reproduce sexually very often. The advantage of obligate sex becomes larger in the absence of recombination. Surprisingly, obligate sex can take over even when the population has a lower mean fitness as a result. We show that this is due to the high success of obligate males that can compensate the cost of sex.