  The next-to-next-to-leading order (NNLO) pQCD prediction for the
$\gamma\gamma^* \to \eta_c$ form factor was evaluated in 2015 using
nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction
and the BaBar measurements was observed. Until now there has been no solution
for this puzzle. In this paper, we present a NNLO analysis by applying the
Principle of Maximum Conformality (PMC) to set the renormalization scale. By
carefully dealing with the light-by-light diagrams at the NNLO level, the
resulting high precision PMC prediction agrees with the BaBar measurements
within errors, and the conventional renormalization scale uncertainty is
eliminated. The PMC is consistent with all of the requirements of the
renormalization group, including scheme-independence. The application of the
PMC thus provides a rigorous solution for the $\gamma\gamma^* \to \eta_c$ form
factor puzzle, emphasizing the importance of correct renormalization
scale-setting. The results also support the applicability of NRQCD to hard
exclusive processes involving charmonium.
