Over this century, coral reefs will run the gauntlet of climate change, as marine heatwaves (MHWs) become more intense and frequent, and ocean acidification (OA) progresses. However, we still lack a quantitative assessment of how, and to what degree, OA will moderate the responses of corals to MHWs as they intensify throughout this century. Here, we first projected future MHW intensities for tropical regions under three future greenhouse gas emissions scenario (representative concentration pathways, RCP2.6, RCP4.5 and RCP8.5) for the near-term (2021–2040), mid-century (2041–2060) and late-century (2081–2100). We then combined these MHW intensity projections with a global data set of 1,788 experiments to assess coral attribute performance and survival under the three emissions scenarios for the near-term, mid-century and late-century in the presence and absence of OA. Although warming and OA had predominately additive impacts on the coral responses, the contribution of OA in affecting most coral attributes was minor relative to the dominant role of intensifying MHWs. However, the addition of OA led to greater decreases in photosynthesis and survival under intermediate and unrestricted emissions scenario for the mid- and late-century than if intensifying MHWs were considered as the only driver. These results show that role of OA in modulating coral responses to intensifying MHWs depended on the focal coral attribute and extremity of the scenario examined. Specifically, intensifying MHWs and OA will cause increasing instances of coral bleaching and substantial declines in coral productivity, calcification and survival within the next two decades under the low and intermediate emissions scenario. These projections suggest that corals must rapidly adapt or acclimatize to projected ocean conditions to persist, which is far more likely under a low emissions scenario and with increasing efforts to manage reefs to enhance resilience.