Background Multiple animal species exhibit morphological asymmetries in male genitalia. In insects, left-right genital asymmetries evolved many times independently and have been proposed to appear in response to changes in mating position. However, little is known about the relationship between mating position and the interaction of male and female genitalia during mating, and functional analyses of asymmetric morphologies in genitalia are virtually non-existent. We investigated the relationship between mating position, asymmetric genital morphology and genital coupling in the fruit fly Drosophila pachea, in which males possess an asymmetric pair of external genital lobes and mate in an unusual right-sided position on top of the female. Results We examined D. pachea copulation by video recording and by scanning electron microscopy of genital complexes. We observed that the interlocking of male and female genital organs in D. pachea is remarkably different from genital coupling in the well-studied D. melanogaster. In D. pachea, the female oviscapt valves are asymmetrically twisted during copulation. The male’s asymmetric lobes tightly grasp the female’s abdomen in an asymmetric ‘locking’ position, with the left and right lobes contacting different female structures. The male anal plates, which grasp the female genitalia in D. melanogaster, do not contact the female in D. pachea. Experimental lobe amputation by micro-surgery and laser-ablation of lobe bristles led to aberrant coupling of genitalia and variable mating positions, in which the male was tilted towards the right side of the female. Conclusion We describe, for the first time, how the mating position depends on coupling of male and female genitalia in a species with asymmetric genitalia and one-sided mating position. Our results show that D. pachea asymmetric epandrial lobes do not act as a compensatory mechanism for the change from symmetric to one-sided mating position that occurred during evolution of D. pachea’s ancestors, but as holding devices with distinct specialized functions on the left and right sides. Electronic supplementary material The online version of this article (doi:10.1186/s12862-016-0747-4) contains supplementary material, which is available to authorized users.