Abstract: We explore a new approach for completing the universal set of logic gates in two dimensions by transforming the codestates of a few copies of the toric/surface code into a non-Abelian topological phase and subsequently reversing the operation. We propose several concrete fault-tolerant protocols that realize magic state preparation and non-Clifford unitary gates. At the circuit level, these protocols are quite simple: they involve few-qubit Pauli measurements, on-site (or three-qubit nearest-neighbor, depending on the geometry) non-Clifford unitary gates and Pauli and Clifford corrections following from the just-in-time decoding. These results constitute a new approach to universal topological quantum computation in two dimensions without anyon braiding or magic state distillation.