Many socially monogamous species paradoxically show signs of strong sexual selection, suggesting cryptic sources of sexual competition among males. Darwin argued that sexual selection could operate in monogamous systems if breeding sex ratios are biased or if some males attract highly fecund females. Alternatively, sexual selection might result from promiscuous copulations outside the pair bond, although several recent studies have cast doubt on this possibility, in particular by showing that variance in apparent male reproductive success (number of social young) differs little from variance in actual male reproductive success (number of young sired). Our results from a long-term study of the socially monogamous splendid fairy-wren (Malurus splendens) demonstrate that such comparisons are misleading and do not adequately assess the effects of extra-pair paternity (EPP). By partitioning the opportunity for selection and calculating Bateman gradients, we show that EPP has a strong effect on male annual and lifetime fitness, whereas other proposed mechanisms of sexual selection do not. Thus, EPP drives sexual selection in this, and possibly other, socially monogamous species.