  We demonstrate that Borel QCD sum rules for heavy-light currents entail a
very strong correlation between the $b$-quark mass $m_b$ and the $B$-meson
decay constant $f_B,$ that is, $\delta f_B/f_B\approx-8\delta m_b/m_b.$ By
starting from $f_B$ as input, this observation allows for an accurate sum-rule
determination of $m_b.$ Employing precise lattice QCD results for $f_B$ in our
sum-rule study based on the three-loop $O(\alpha_s^2)$ heavy-light correlation
function implies $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$ GeV for the $b$-quark
$\bar{\rm MS}$ mass.
