The vast variation observed in genital morphology is a longstanding puzzle in evolutionary biology. Studies showing that the morphology of the mammalian baculum (penis bone) can covary with a male’s paternity success indicate a potential impact of baculum morphology on male fitness, likely through influencing sperm competition outcomes. We therefore measured the size (measurements of length and width) and shape (geometric morphometric measurements) of the bacula of male house mice used in previously published sperm competition experiments, in which two males mated successively with the same female in staged matings. This enabled us to correlate baculum morphology with sperm competition success, incorporating potential explanatory variables related to copulatory plugs, male mating behavior and a selfish genetic element that influences sperm motility. We found that a wider baculum shaft increased a male’s paternity share when mating first, but not when mating second with a multiply-mating female. Geometric morphometric shape measurements were not clearly associated with fertilization success for either male. We found limited evidence that the effect of baculum morphology on male fertilization success was altered by experimental removal of the copulatory plug. Furthermore, neither genetic differences in sperm motility, nor covariation with male mating behavior mediated the effect of baculum morphology on male fertilization success. Taken together with previous findings, the mating-order effects we found here suggest that baculum-mediated stimulation by the first male might be particularly important for fertilization.