Price, who scored 27 and 28 points in La Salle's first two games this season, made 11 of 14 shots from the floor and was 5 of 7 from the free throw line.
Tony Washington, who made 6 of 8 field goal attempts, finished with 14 points and nine rebounds. Cleon Roberts added 10 points and Rohan Brown chipped in six points and grabbed 11 rebounds for La Salle (3-0).
Lafayette (1-3), which beat Saint Peter's 87-86 in overtime on Sunday for its first victory, struggled on the boards as the Explorers won that battle 43-25.
La Salle was up 44-41 at the break and led 69-52 midway of the second half. Lafayette made a late run 13-3 run but could not catch the Explorers.