The Senate's final vote was 53-42, but the key was an earlier cloture vote that squeaked by with 60 votes only after Sen. Lisa Murkowski, R-Alaska, agreed to change her position and a delay to give Sen. Heidi Heitkamp, D-N.D., time to return to Washington, The Washington Post reported.
Heitkamp's arrival about 7 p.m. EDT allowed the measure to avoid a Republican filibuster and proceed to the up-and-down vote.
Jones, a U.S. attorney in Minneapolis, becomes the bureau's first confirmed leader in seven years, the Post noted.
"This position hasn't had a director for seven years and it's way past time that the job is finally filled," Heitkamp said in a statement. "Mr. Jones has strong credentials."
The other Republicans who voted for cloture were Sens. Kelly Ayotte of New Hampshire, Susan Collins of Maine, Lindsey Graham of South Carolina, Mark Kirk of Illinois and John McCain of Arizona, the Post said.
Jones' appointment by President Obama in January had run into strong headwinds from some GOP senators including Chuck Grassley of Iowa, who criticized his handling of cases as a federal prosecutor and his treatment of whistle-blowers.