We report on spin Hall magnetoresistance (SMR) and spin Seebeck effect (SSE) in a single crystal of the rare-earth antiferromagnet DyFeO3 with a thin Pt film contact. The angular shape and symmetry of the SMR at elevated temperatures reflect the antiferromagnetic order of the Fe3+ moments as governed by the Zeeman energy, the magnetocrystalline anisotropy, and the Dzyaloshinskii-Moriya interaction. We interpret the observed linear dependence of the signal on the magnetic field strength as evidence for field-induced order of the Dy3+ moments up to room temperature. At and below the Morin temperature of 50 K, the SMR monitors the spin-reorientation phase transition of Fe3+ spins. Below 23 K, additional features emerge that persist below 4 K, the ordering temperature of the Dy3+ magnetic sublattice. We conclude that the combination of SMR and SSE is a simple and efficient tool to study spin reorientation phase transitions and sublattice magnetizations.