Tilman Dunbar scored 13 points, Jace Hogan added 10, and Will Kelly had three blocks for Navy (9-4), which outshot Furman 42 percent to 30 percent and outrebounded them 41-28, including 12-7 on the offensive end.
Furman led briefly, but Shawn Anderson's jumper and 3-pointer sparked a 24-2 run and Navy led 29-11. Hogan scored nine-straight points and Navy led 36-18 at halftime.
Anderson had four of Navy's 14 assists, and Hogan and Tom Lacey each grabbed eight rebounds.
Furman used an 11-1 run to close within 58-47 with 2:38 to play and outscored the Midshipmen 31-26 in the half, but Hogan hit a free throw to seal it for Navy and time expired.