The Hornets have won three in a row for the first time since they captured 10 straight in January.
Green wound up missing his last five shots over the game's final 6 minutes, but he scored 31 points off the bench. He hit 5-of-6 from 3-point range.
New Orleans began the evening a half game behind Portland in the race for the No. 6 seed in the Western Conference. Carl Landry contributed 17 points for New Orleans and also made his first eight tries. The Hornets shot 55 percent overall.
Phoenix slipped to 1-3 on a five-game road trip. The Suns, who had a 10-point lead in the first period, was led by 18 points by Jared Dudley.