The tilt of Saturn's spin axis to its orbit plane is 26.7d, while that of Jupiter is only 3.1d. We offer an explanation for this puzzling difference owing to gravitational perturbations of Saturn by the planet Neptune. A similarity between the precession period of Saturn's spin axis and the 1.87×106 yr precession period of Neptune's slightly inclined orbit plane implicates a resonant interaction between these planets as responsible for tilting Saturn from an initially more upright state. We make a case that Saturn was captured into this resonance during the erosion of the Kuiper belt, which decreased the rate of regression of Neptune's orbit plane. Penetrating the resonance pumped up Saturn's obliquity to its current value. The spin axis may also be librating in the resonance with an amplitude ψ>~31deg, and we discuss possible causes of this and the implied constraint on Saturn's moment of inertia. Matching the current pole position to the predicted outcome could place constraints on early solar system processes.