In this paper, we first document a new empirical finding by showing that the European Central Bank’s (ECB) monetary policy decisions significantly influence global energy prices. Through Lucas-critique-robust counterfactual analysis, we then empirically study the implications of this result for the transmission of monetary policy. Our findings reveal that a central bank’s ability to affect energy prices strengthens and accelerates the monetary transmission to inflation dynamics, and alleviates the inflation-output trade-off. We illustrate the relevance of these results by examining their role in the optimal policy response to an energy supply shock. Our estimates show that monetary policy’s ability to affect global energy prices effectively halves the necessary tightening to stabilize inflation and the corresponding economic contraction, compared to a scenario in which energy prices are unaffected by monetary policy.