It was the first time Auburn (4-5) has won consecutive games this season after also beating Grambling 92-42 on Dec. 11. Furman fell to 3-6.
Denson scored 12 of his points in the first half as the Tigers took a 35-20 lead. Senior guard and Southeastern Conference-leading scorer Frankie Sullivan had seven points in the first half and finished with 11 points.
Price was 4 for 4 on 3-pointers and is 8 for 8 from behind the arc in his last two games.
Auburn transfer center Asauhn Dixon-Tatum, playing extended minutes with starting center Rob Chubb in foul trouble, had a career-high nine rebounds with six points. Each of Dixon-Tatum's rebounds came in the first half.
Auburn weathered an early 7-2 deficit, finishing the first half on a 12-3 run. Furman guard Bobby Austin tipped a loose ball into Auburn's basket at the first-half buzzer, and the points were awarded to Sullivan.
Auburn made 8 of 17 (47.7 percent) 3-pointers in the first half, while Furman struggled to bust the Tigers' zone defense on the other end. The Paladins shot 16 for 52 (30.8 percent) from the field, and 5 of 22 (22.7 percent) from behind the arc.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.