We present a fully differential and high-precision calculation of top-quark pair-production and decay at the LHC, providing predictions for observables constructed from top-quark leptonic and b-flavored jet final states. The calculation is implemented in a parton-level Monte Carlo and includes an approximation to the next-to-next-to-leading-order (NNLO) corrections to the production and, for the first time, the exact NNLO corrections to the decay subprocesses. The corrections beyond NLO are sizable, and including them is crucial for an accurate description of the cross section constrained by experimental phase-space restrictions. We compare our predictions to published ATLAS and CMS measurements at the LHC, finding improved agreement compared with lower orders in the perturbative expansion.