Davis hit 10-of-13 shots from the field and scored 23 points for the Wildcats, who are laden with young talent and will be among the favorites this year to capture the national title.
Marquis Teague, another freshman, scored 16 points and Doron Lamb had 15 points to go with eight assists and five rebounds.
Kentucky is coming off a Final Four season in which it lost to eventual champion Connecticut by a point in the national semifinals.
Marist, which has won just seven times over the last two seasons, was led by Isaiah Morton with 13 points.
The Red Foxes played Kentucky even for the first 9 minutes before falling behind at the break 45-36. Kentucky scored the first six points of the second half to turn the game into a rout.
Kentucky shot 61 percent from the field to 31 percent for Marist.