Cousins hit five 3-pointers, tying a career high. He made five shots inside while being fouled for three-point plays and had the jubilant home crowd chanting his nickname, "Boogie."
Cousins also blocked three shots and assisted on Anthony Davis' crowd-pleasing alley-oop dunk.
Davis added 19 points and 13 rebounds for the Pelicans, who won for the fifth time in six games while snapping Memphis' four-game winning streak.
Mikes Conley 16 scored points for Memphis, while JaMychal Green and Troy Daniels each scored 12.
Memphis led by 12 in the first half, but New Orleans surged ahead with a 21-0 run in the third quarter.
