BubR1 insufficiency occurs with natural aging and induces progeroid phenotypes in both mice and children with mosaic variegated aneuploidy syndrome. In response to BubR1 insufficiency, skeletal muscle, fat, and lens tissue engage p19^Arf to attenuate senescence and age-related deterioration. Here, we address how p19^Arf exerts this caretaker role using BubR1 progeroid mice lacking p53 or its transcriptional target p21. We show that p53 delays functional decline of skeletal muscle and fat in a p21-dependent fashion by inhibiting p16^Ink4a-mediated senescence of progenitor cells. Strikingly, p53 also attenuates the formation of cataractous lenses, but here its antiaging effect is p21 independent, as we found p21 to promote senescence of lens epithelial cells and cataract formation. Together, these results demonstrate that p53 counteracts tissue destruction in response to BubR1 insufficiency through diverse mechanisms and uncover a causal link between senescence of the progenitor cell compartment and age-related dysfunction.