The United States Senate voted on Wednesday to confirm Neomi Rao, President Trump’s nominee to replace Brett M. Kavanaugh on a key appeals court, bringing the president closer to his goal of putting his stamp firmly on the federal judiciary.

Ms. Rao, the administrator of the White House Office of Information and Regulatory Affairs, was confirmed by a vote of 53 to 46 for a seat on the United States Court of Appeals for the District of Columbia Circuit, a frequent steppingstone to the Supreme Court.

A former law professor and clerk for Justice Clarence Thomas, Ms. Rao was seen as an ally in the president’s push for deregulation and had the backing of the Federalist Society, the powerful conservative legal group.

Lindsey Graham, Republican of South Carolina and the chairman of the Senate Judiciary Committee, praised Ms. Rao when the committee moved her nomination forward earlier this month.