Spintronic devices based on antiferromagnetic (AFM) materials hold the promise of fast switching speeds and robustness against magnetic fields(1-3). Different device concepts have been predicted(4,5) and experimentally demonstrated, such as low-temperature AFM tunnel junctions that operate as spin-valves(6), or room-temperature AFM memory, for which either thermal heating in combination with magnetic fields(7) or Neel spin-orbit torque(8) is used for the information writing process. On the other hand, piezoelectric materials were employed to control magnetism by electric fields in multiferroic heterostructures(9-12), which suppresses Joule heating caused by switching currents and may enable low-energy-consuming electronic devices. Here, we combine the two material classes to explore changes in the resistance of the high-Neel-temperature antiferromagnet MnPt induced by piezoelectric strain. We find two non-volatile resistance states at room temperature and zero electric field that are stable in magnetic fields up to 60 T. Furthermore, the strain-induced resistance switching process is insensitive to magnetic fields. Integration in a tunnel junction can further amplify the electroresistance. The tunnelling anisotropic magnetoresistance reaches similar to 11.2% at room temperature. Overall, we demonstrate a piezoelectric, strain-controlled AFM memory that is fully operational in strong magnetic fields and has the potential for low-energy and high-density memory applications.