Using the near universe of online vacancy postings in the U.S., we study the interaction between labor market power and monetary policy. We show empirically that labor market power amplifies the labor demand effects of monetary policy, while not disproportionately affecting wage growth. A search and matching model in which firms can attract workers by either offering higher wages or posting more vacancies can rationalize these findings. We also find that vacancy postings that do not require a college degree or technology skills are more responsive to monetary policy, especially when firms have labor market power. Our results help explain the "wageless" recovery after the 2008 financial crisis and the flattening of the wage Phillips curve, especially for the low-skilled, who saw stagnant wages but a robust decline in unemployment.