The Warriors snapped a four-game losing streak but have won four of their last five road contests.
With Golden State having traded away Monta Ellis, the rookie Thompson has moved into the starting lineup. In his third career start, he made four of Golden State's 14 shots from 3-point range.
His previous career high point production had been 26 last week against Boston, the only other time he has reached the 20-point mark.
David Lee added 25 points with 11 rebounds for the Warriors, who pulled away late after having a three-point lead to start the fourth quarter.
The Hornets were led by the first triple-double in the career of Jarrett Jack -- 17 points, 11 assists and 10 rebounds. New Orleans has lost four of five.