  We study the triply heavy baryons $\Omega_{QQQ}$ $(Q=c, b)$ in the QCD Sum
Rules by calculating the next-to-leading order (NLO) contribution in 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
$\Omega_{QQQ}$, for it not only leads to a large correction, but also reduces
the parameters dependence and makes 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. In particular, due to the inclusion
of the NLO contribution, the renormalization schemes ($\overline{\rm{MS}}$ and
On-Shell) dependence and scale dependence are significantly improved. As a
result, after including the NLO contribution of the perturbative part in QCD
sum rules, the masses are predicted 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 that from the variation
of the renormalization scale $\mu$ in the range $(0.8-1.2) M_B$. A careful
study for the $\mu$ dependence in a wider range is further performed, which
shows that the LO results are very sensitive to the choice of $\mu$ whereas the
NLO results are much better. In addition to the $\mu=M_B$ result, a quite
stable value, (4.75-4.80) GeV, for the $\Omega_{ccc}$ mass is found in the
range of $\mu=(1.2-2.0) M_B$.
