We report magnetic and calorimetric measurements down to T = 1 mK on the canonical heavy-electron metal YbRh2Si2. The data reveal the development of nuclear antiferromagnetic order slightly above 2 mK. The latter weakens the primary electronic antiferromagnetism, thereby paving the way for heavy-electron superconductivity below Tc = 2 mK. Our results demonstrate that superconductivity driven by quantum criticality is a general phenomenon.