Davis finished with 27 points overall and also grabbed 10 rebounds for New Orleans, which ran out the clock to seal the win after Marc Gasol had split a pair of free throws with 29.9 seconds left, pulling Memphis within three points.
Tyreke Evans also heated up down the stretch for the Pelicans, scoring 11 of his 15 points in the fourth quarter.
The Grizzlies had their five-game winning streak ended despite 23 points and 20 rebounds from Zach Randolph.
Millions of Getty images now available for free via embed tool
Ray Liotta sues skin care company over use of likeness