Davis scored 22 points to help the Pelicans put together back-to-back wins for the second time this season.
Utah lost its fourth in a row and has only one victory in 13 outings.
Ryan Anderson scored 19 points off the bench for the Pelicans and Jrue Holiday added 14. New Orleans had lost its four previous meetings with the Jazz.
Enes Kanger delivered 19 points and nine rebounds for Utah. Gordon Hayward, who was averaging 18 points a game coming into the contest and is his team's leading scorer, made just 1-of-17 attempts from the field and was held to six points.