Rational material design can accelerate the discovery of materials with improved functionalities. This approach can be implemented in Heusler compounds with tunable magnetic sublattices to demonstrate unprecedented magnetic properties. Here, we have designed a family of Heusler alloys with a compensated ferrimagnetic state. In the vicinity of the compensation composition in Mn-Pt-Ga, a giant exchange bias (EB) of more than 3 T and a large coercivity are established. The large exchange anisotropy originates from the exchange interaction between the compensated host and ferrimagnetic clusters that arise from intrinsic anti-site disorder. Our design approach is also demonstrated on a second material with a magnetic transition above room temperature, Mn-Fe-Ga, exemplifying the universality of the concept and the feasibility of room-temperature applications. These findings may lead to the development of magneto-electronic devices and rare-earth-free exchange-biased hard magnets, where the second quadrant magnetization can be stabilized by the exchange bias.