  Motivated by the recent experimental data, we have revisited the $B\to \pi
K,\pi \pi$ decays in the framework of QCD factorization, with inclusion of the
important strong penguin corrections of order $\alpha_s^2$ induced by $b\to D
g^\ast g^\ast$ ($D=d$ or $s$ and $g^\ast$ denotes an off-shell gluon)
transitions. We find that these higher order strong penguin contributions can
provide $\sim 30%$ enhancement to the penguin-dominated $B\to \pi K$ decay
rates, and such an enhancement can improve the consistency between the
theoretical predictions and the experimental data significantly, while for the
tree-dominated $B\to \pi\pi$ decays, these higher order contributions play only
a minor role. When these strong penguin contributions are summed, only a small
strong phase remains and the direct CP asymmetries get small corrections. We
also find patterns of the ratios between the CP-averaged branching fractions
remain nearly unaffected even after including these higher order corrections
and the $\pi K$ puzzle still persists. Our results may indicate that to resolve
the puzzle one would have to resort to new physics contributions in the
electroweak penguin sector as found by Buras {\it et al}.
