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Dirac semi-metals are a class of topological materials wherein both time-reversal symmetry and inversion symmetry co-exist. The application of a gate-voltage breaks inversion symmetry while magnetic field breaks time-reversal symmetry. This leads to changes in the symmetries of the ground state Hamiltonian, manifested through distinct signatures in universal conductance fluctuations which we probe here in nanowires of the prototypical Dirac semi-metal Cd₃As₂. We find a factor of √2 reduction in the magnitude of the universal conductance fluctuations as the magnetic field is increased, due to breaking time-reversal symmetry. In contrast, the magnitude of the fluctuations increases by a factor of 2√2 away from the charge neutrality point. Our experiments provide unequivocal evidence of universal conductance fluctuations as the source of intrinsic fluctuations in quantum transport measurements in mesoscopic Cd₃As₂ devices and establishes the usefulness of such measurements as a tool for probing topological phase transitions.