This verse describes the fruit of the prasāda (serenity) promised in the previous verse. The logic is beautifully simple: when the mind is truly serene — free from the push and pull of attraction and aversion — suffering ceases. Not because circumstances change, but because the mind no longer generates suffering through resistance, craving, and reaction. 'Sarvaduḥkhānāṃ hāniḥ' (the destruction of all sorrows) is a comprehensive promise: not the reduction of some sorrows, but the end of all suffering. The second line adds a crucial insight: a serene mind naturally stabilizes the intellect. 'Paryavatiṣṭhate' means the buddhi becomes firmly established, rooted, unwavering. The word 'āśu' (quickly) is significant — Krishna is saying that once serenity is achieved, the higher faculties stabilize rapidly. This creates a positive feedback loop: serenity leads to stable intellect, stable intellect reinforces serenity, and the cycle builds upon itself. This is the exact reverse of the destructive chain described in verses 62-63 and represents the ascending spiral of spiritual growth.