Thornton made his first five shots and 10 of 13 in the quarter as the Hornets scored 40 points to turn an eight-point first-quarter deficit into a 56-53 lead at the half. New Orleans shot 71 percent for the quarter, making 17 of 24 shots.
Thornton cooled a little in the second half and finished with a career-high 37 points on 15-of-22 shooting. The Hornets lost the game as well 105-95.
Peja Stojakovic previously held the mark by scoring 22 in the first quarter against Charlotte on Nov. 14, 2007. He had nine points on Tuesday.
Thornton is a second-round pick out of LSU. In one quarter he nearly matched his former career high for a game of 25. He entered the game averaging 10.8 points this season.
Information from The Associated Press was used in this report.