We study the possibility of generating baryon asymmetry of the universe from WIMP dark matter (DM) annihilations during non-standard cosmological epochs. Adopting a minimal particle physics model to realise this along with non-zero light neutrino masses, we consider two different types of non-standard cosmic history namely, (i) fast expanding universe and (ii) early matter domination. We find that the allowed parameter space is consistent with DM relic and observed baryon asymmetry gets enlarged with the possibility of lower DM mass in some scenarios. While much lighter DM can face further scrutiny at direct search experiments, the non-standard epochs offer complementary probes on their own.