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We present a resummed QCD calculation of the thrust distribution in electron-positron annihilation in the back-to-back region up to N^4LL accuracy, matched to fixed-order results up to NNLO. We perform the resummation of the large Sudakov logarithms in the Laplace-conjugated space, and we show that the results differ significantly from those obtained through resummation in thrust space. We include non-perturbative corrections using an analytic hadronization model that depends on two free parameters. Finally, we present a comparison of our predictions with experimental data at the Z-boson peak, and we extract a value for the QCD coupling that is fully consistent with the world average.