Chemically synthesized semiconductor quantum dots (QDs) can potentially enable solution-processable laser diodes with a wide range of operational wavelengths, yet demonstrations of lasing from the QDs are still at the laboratory stage. An important challenge-realization of lasing with electrical injection-remains unresolved, largely due to fast nonradiative Auger recombination of multicarrier states that represent gain-active species in the QDs. Here we present population inversion and optical gain in colloidal nanocrystals realized with direct-current electrical pumping. Using continuously graded QDs, we achieve a considerable suppression of Auger decay such that it can be outpaced by electrical injection. Further, we apply a special current-focusing device architecture, which allows us to produce high current densities (j) up to ∼18 A cm-2 without damaging either the QDs or the injection layers. The quantitative analysis of electroluminescence and current-modulated transmission spectra indicates that with j = 3-4 A cm-2 we achieve the population inversion of the band-edge states.