James came within three assists of a triple-double in carrying the Cavaliers to their third victory in four games.
Atlanta opened the fourth quarter with a 16-4 run to take a one-point lead. With the score tied at 89-89, Damon Jones scored on a layup to start 7-2 Cleveland rush that gave the Cavaliers a 96-91 lead with a minute to play.
Atlanta was led by 23 points from Joe Johnson. The Hawks had won their previous three games.
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