Anderson made five 3-pointers and hauled down nine rebounds.
Darius Miller contributed 16 points for New Orleans, which notched its third straight home win. Roger Mason Jr. (14 points), Anthony Davis (14, six rebounds) and Brian Roberts (13, 18 assists) also reached double figures for the Hornets.
Denver got 24 points from Danilo Gallinari but couldn't avoid the end of its streak, which finished one short of breaking the franchise's 1969-70 record.
Kenneth Faried added 13 points and seven rebounds for the Nuggets.
Notable deaths of 2014 [PHOTOS]