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We demonstrate that Borel QCD sum rules for heavy-light currents entail a very strong correlation between the b-quark mass mb and the B-meson decay constant fB, that is, δfB/fB≈−8δmb/mb. By starting from fB as input, this observation allows for an accurate sum-rule determination of mb. Employing precise lattice QCD results for fB in our sum-rule study based on the three-loop O(α2s) heavy-light correlation function implies mb(mb)=(4.247±0.034) GeV for the b-quark MSbar mass.