The game was tied after each of the first three periods but the Hornets prevailed to snap a two-game losing streak.
Jarrett Jack hit a 3-pointer for New Orleans to give the Hornets an eight-point lead with 2:59 to play, and they protected their advantage at the foul line down the stretch.
Chris Paul scored 23 points and had 14 assists for the Hornets, who began the night in sixth place in the Western Conference.
Memphis, which has lost two out of three, was led by 20 points and 11 rebounds from Zach Randolph.
Notable deaths of 2014 [PHOTOS]