Ocean warming and acidification from increasing levels of atmospheric CO₂ represent major global threats to coral reefs, and are in many regions exacerbated by local‐scale disturbances such as overfishing and nutrient enrichment. Our understanding of global threats and local‐scale disturbances on reefs is growing, but their relative contribution to reef resilience and vulnerability in the future is unclear. Here, we analyse quantitatively how different combinations of CO₂ and fishing pressure on herbivores will affect the ecological resilience of a simplified benthic reef community, as defined by its capacity to maintain and recover to coral‐dominated states. We use a dynamic community model integrated with the growth and mortality responses for branching corals (Acropora) and fleshy macroalgae (Lobophora). We operationalize the resilience framework by parameterizing the response function for coral growth (calcification) by ocean acidification and warming, coral bleaching and mortality by warming, macroalgal mortality by herbivore grazing and macroalgal growth via nutrient loading. The model was run for changes in sea surface temperature and water chemistry predicted by the rise in atmospheric CO₂ projected from the IPCC's fossil‐fuel intensive A1FI scenario during this century. Results demonstrated that severe acidification and warming alone can lower reef resilience (via impairment of coral growth and increased coral mortality) even under high grazing intensity and low nutrients. Further, the threshold at which herbivore overfishing (reduced grazing) leads to a coral–algal phase shift was lowered by acidification and warming. These analyses support two important conclusions: Firstly, reefs already subjected to herbivore overfishing and nutrification are likely to be more vulnerable to increasing CO₂. Secondly, under CO₂ regimes above 450–500 ppm, management of local‐scale disturbances will become critical to keeping reefs within an Acropora‐rich domain.