  We apply the renormalization group optimized perturbation theory (RGOPT) to
evaluate the quark contribution to the QCD pressure at finite temperatures and
baryonic densities, at next-to-leading order (NLO). Our results are compared to
NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and
hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a
nonperturbative approximation, exhibiting a drastically better remnant
renormalization scale dependence than pQCD, thanks to built-in renormalization
group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed
quark contributions the purely perturbative NLO glue contribution, our results
show a remarkable agreement with ab initio lattice simulation data for
temperatures $0.25 \lesssim T \lesssim 1 \, {\rm GeV}$, with a remnant scale
dependence drastically reduced as compared to HTLpt.
