We present a high-precision resummed QCD calculation of the thrust distribution in electron-positron annihilation in the back-to-back region. The resummation of large Sudakov logarithms is performed in Laplace space, yielding results that differ significantly from those obtained through traditional methods in thrust space. We validate our approach with an analytic formula for the inverse Laplace transform based on the saddle-point approximation. Non-perturbative corrections are included via an analytic hadronization model with two free parameters. Finally, we compare our predictions with experimental data at the Z-boson resonance, extracting a value for the strong coupling that is fully consistent with the world average, thus resolving a long-standing tension in the literature.