We empirically show that a central bank’s ability to affect global energy prices crucially alters monetary policy transmission. We first provide novel evidence that euro area monetary policy significantly affects energy prices. Employing a Lucas critique-robust counterfactual framework, we find that this ability strengthens and accelerates transmission to inflation and substantially alleviates the inflation-output trade-off. We further show that this ability materially shapes the mandate-optimal policy response to an energy supply shock: the optimal response implies a smaller interest rate increase and a more favorable inflation-output allocation than in a scenario where energy prices are unaffected by monetary policy.