We compute the third-order corrections to the heavy quarkonium
spectrum and production/annihilation rates due to the leading
renormalization group running of the static potential. The previously
known complete ${\cal O}(m_q\alpha_s^5)$ result for the heavy
quarkonium ground state energy is extended to the exited states.
After including the ${\cal O}(\alpha_s^3)$ corrections the
perturbative results are in surprisingly good agreement with the
experimental data on the masses of the excited $\Upsilon$ resonances
and the leptonic width of the $\Upsilon(1S)$ meson. The impact of the
corrections on the $\Upsilon$ sum rules and top quark-antiquark
threshold production cross section is also discussed.