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Exchange bias is a property of widespread technological utility, but its underlying mechanism remains elusive, in part because it is rooted in the interaction of coexisting order parameters in the presence of complex magnetic disorder. Here we show that a giant exchange bias housed within a spin-glass phase arises in a disordered antiferromagnet. The magnitude and robustness of the exchange bias emerges from a convolution of two energetic landscapes, namely the highly degenerate landscape of the spin glass biased by the sublattice spin configuration of the antiferromagnet. The former provides a source of uncompensated moment, whereas the latter provides a mechanism for its pinning, which leads to the exchange bias. Tuning the relative strengths of the spin-glass and antiferromagnetic order parameters reveals a principle for tailoring the exchange bias, with potential applications to spintronic technologies. Coexistence of a spin-glass phase with antiferromagnetism in an intercalated crystal produces a large exchange bias effect. This is due to the interplay of disorder and frustration.