The entire worldliness stands conquered by those, whose mind is established in equal vision. Brahman is taintless and equal. Therefore, by attaining equality, they become established in Brahman.
Here Krishna does not refer to Soul or God. Yet he delivers the full spiritual message, a point all should absorb with special attention.
Equanimity is the crux of spirituality. See how it makes one pure, wholesome and fulfilled. The entire world and our interactions with it, bring only two experiences, sukha and duhkha. All dvandvas, pairs of opposites, verily fetch only sukha-duhkhas. So, evenness to them virtually means conquest of the world. See how samatva (equipoise) of the mind means victory over the world.
Krishna says that such evenness is the core of spirituality, especially for those given to introspection. Brahman, the supreme Reality, is the goal of all spiritual seekers. Brahman is equalness, free of any blemish. Therefore, those whose mind is established in equalness verily abide in Brahman. They become taintless and free.