Davis posted 24 points, nine rebounds and six blocks for the Pelicans, who picked up a crucial game in the win column to stay alive in the Western Conference playoff race. Tyreke Evans had 25 points and 10 assists and Quincy Pondexter scored 16 points to help end a four-game losing skid.
The win put New Orleans in a tie with Phoenix for ninth place in the West, three games behind eighth-seeded Oklahoma City. The Suns are in action Friday against Portland.
Cousins put up a monster line with 39 points and 20 rebounds and Rudy Gay netted 18 points, but the rest of the Kings lineup contributed just 31 combined points on 12-of-33 shooting.
The Kings had won four straight games, one shy of matching a season high.
Cousins had 23 points on 10-of-14 shooting and Davis went 3-for-14 in the first half, but the Pelicans still owned a 46-42 advantage at the break.
Gay scored seven straight Kings points after Ben McLemore put the visitors in front early in the third with a 3-pointer, but Pondexter drilled consecutive 3s at the other end to restore the Pelicans' lead.
Evans scored twice during an 8-0 run later in the period that made it 74-63. The lead grew to 18 in the fourth as the Pelicans coasted to the finish line.
Norris Cole scored 12 points for New Orleans and Omer Asik grabbed 12 rebounds ... The Pelicans won the rebounding margin, 47-37 ... Nik Stauskas, recently nicknamed "Sauce Castillo" due to a closed captioning error that went viral, had five points to lead Sacramento's reserves. The Pelicans' bench outscored their counterparts, 29-12.