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The asteroid belt is characterized by an extreme low total mass of material on dynamically excited orbits. The Nice model explains many peculiar qualities of the Solar system, including the belt’s excited state, by invoking an orbital instability between the outer planets. However, previous studies of the Nice model’s effect on the belt’s structure struggle to reproduce the innermost asteroids’ orbital inclination distribution. Here, we show how the final phase of giant planet migration sculpts the asteroid belt, in particular its inclination distribution. As interactions with leftover planetesimals cause Saturn to move away from Jupiter, its rate of orbital precession slows as the two planets’ mutual interactions weaken. When the planets approach their modern separation, where Jupiter completes just short of five orbits for every two of Saturn’s, Jupiter’s eccentric forcing on Saturn strengthens. We use numerical simulations to show that the absence of asteroids with orbits that precess between 24 and 28 arcsec yr−1 is related to the inclination problem. As Saturn’s precession speeds back up, high-inclination asteroids are excited on to planet crossing orbits and removed from the inner main belt. Through this process, the asteroid belt’s orbital structure is reshaped, leading to markedly improved simulation outcomes.