  We study the triply heavy baryons $\Omega_{QQQ}$ $(Q=c, b)$ in the QCD sum
rules by performing the first calculation of the next-to-leading order (NLO)
contribution to the perturbative QCD part of the correlation functions.
Compared with the leading order (LO) result, the NLO contribution is found to
be very important to the $\Omega_{QQQ}$. This is because the NLO not only
results in a large correction, but also reduces the parameter dependence,
making the Borel platform more distinct, especially for the $\Omega_{bbb}$ in
the $\overline{\rm{MS}}$ scheme, where the platform appears only at NLO but not
at LO. Particularly, owing to the inclusion of the NLO contribution, the
renormalization schemes ($\bar {MS}$ and On-Shell) dependence and the scale
dependence are significantly reduced. Consequently, after including the NLO
contribution to the perturbative part in the QCD sum rules, the masses are
estimated to be $4.53^{+0.26}_{-0.11}$ GeV for $\Omega_{ccc}$ and
$14.27^{+0.33}_{-0.32}$ GeV for $\Omega_{bbb}$, where the results are obtained
at $\mu=M_B$ with errors including those from the variation of the
renormalization scale $\mu$ in the range $(0.8-1.2) M_B$. A careful study of
the $\mu$ dependence in a wide range is further performed, which shows that the
LO results are very sensitive to the choice of $\mu$ whereas the NLO results
are considerably better. In addition to the $\mu=M_B$ result, a more stable
value, (4.75-4.80) GeV, for the $\Omega_{ccc}$ mass is found in the range of
$\mu=(1.2-2.0) M_B$, which should be viewed as a more relevant prediction in
our NLO approach because of $\mu$ dependence.
