Davis had 26 points and 17 rebounds and the Pelicans overcame a 17-point first half deficit for their third straight victory and second over the Suns in four days.
Jrue Holiday hit a pair of free throws with 14.5 seconds to give the Pelicans a 116-112 lead and the Suns cut it to two on free throws by Brandon Knight, but Holiday made two more free throws to seal the win in the game that had 17 lead changes.
Eric Gordon had 23 points for New Orleans, former Sun Ish Smith added 20 points and 11 assists, Ryan Anderson also had 20 points, and Holiday finished with 19.
Knight scored 29 points, 20 in the first quarter, and had 10 assists. Leuer added 20 points, 13 in the fourth quarter, and 12 rebounds, and Eric Bledsoe and T.J. Warren each had 18 points.
The Suns, who lost at New Orleans on Sunday night, dropped their third straight to fall to 7-8.