Whispering-gallery-mode resonators have been extensively used in conjunction with different materials for the development of a variety of photonic devices. Among the latter, hybrid structures, consisting of dielectric microspheres and colloidal core/shell semiconductor nanocrystals as gain media, have attracted interest for the development of microlasers and studies of cavity quantum electrodynamic effects. Here we demonstrate single-exciton, single-mode, spectrally tuned lasing from ensembles of optical antenna-designed, colloidal core/shell CdSe/CdS quantum rods deposited on silica microspheres. We obtain single-exciton emission by capitalizing on the band structure of the specific core/shell architecture that strongly localizes holes in the core, and the two-dimensional quantum confinement of electrons across the elongated shell. This creates a type-II conduction band alignment driven by coulombic repulsion that eliminates non-radiative multi-exciton Auger recombination processes, thereby inducing a large exciton-bi-exciton energy shift. Their ultra-low thresholds and single-mode, single-exciton emission make these hybrid lasers appealing for various applications, including quantum information processing.