The stability of supported nanocatalysts is crucial to meeting environmental and energy challenges and necessitates fundamental theory to relieve trial-and-error experimentation and accelerate lab-to-fab translation. Here, we report a Sabatier principle of metal-support interaction for stabilizing metal nanocatalysts against sintering based on the kinetic simulations of 323 metal-support pairs using scaling relations from 1252 energetics data. Too strong of an interaction is shown to trigger Ostwald ripening, whereas too weak of an interaction stimulates particle migration and coalescence. High-throughput screening of supports enables the sintering resistance of nanocatalysts to reach the Tammann temperature on homogeneous supports and far beyond it on heteroenergetic supports. This theory, which is substantiated by first-principles neural network molecular dynamics simulations and experiments, paves the way for the design of ultrastable nanocatalysts.