West scored 20 points in what was the Hornets' fifth straight triumph. New Orleans won in Cleveland for the first time in five seasons.
LeBron James put Cleveland in front with seven seconds remaining by storming past two players in the lane and scoring with a left-handed layup.
After a time out, the Hornets got the ball into the hands of leading scorer Chris Paul, who was quickly triple-teamed. He passed to West, who hit the shot from the top of the circle.
Peja Stojakovic scored 25 points for New Orleans, which began the night tied for the lead in the Western Conference with the Los Angeles Lakers. Paul scored 15 points and had 20 assists with only one turnover.
Zydrunas Ilgauskas scored 29 for Cleveland, which has a three-game lead over Washington for fourth place in the Eastern Conference.