  In this paper, we carry out the next-to-leading-order QCD corrections to $Z
\to \eta_Q+g+g~(Q=c,b)$ (labeled as $gg$) through the color-singlet (CS) state
of $Q\bar{Q}[^1S_0^{[1]}]$, with the aim of assessing the impact of this
process on $Z$ bosons decaying into inclusive $\eta_Q$. We find that the QCD
corrections to the $gg$ process can notably enhance its leading-order results,
especially for the $\eta_c$ case, which would then greatly increase the
existing predictions of $\Gamma_{Z \to \eta_Q+X}$ given by the CS-dominant
process $Z \to \eta_{Q}[^1S_0^{[1]}]+Q+\bar{Q}$. Moreover, with these
significant QCD corrections, the $gg$ process would exert crucial influence on
the CS-predicted $\eta_Q$ energy distributions. In conclusion, in the CS
studies of $Z \to \eta_Q+X$, besides $Z \to \eta_{Q}[^1S_0^{[1]}]+Q+\bar{Q}$,
$Z \to \eta_Q[^1S_0^{[1]}]+g+g$ can provide phenomenologically indispensable
contributions as well.
