Cleveland fended off a late charge from Atlanta to record 104-93 win in the opening game of their NBA Eastern Conference semi-final series.
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The Cavaliers were up by nine points early in the fourth quarter before the Hawks made a run to draw even - the Hawks going basket-for-basket before wilting in the final minutes.
"A win is a win in the post season and we are only going to get better," Cavs superstar LeBron James, who had 25 points, nine assists and seven rebounds, said.
Matthew Dellavedova had a quiet game for the Cavs, spending just 13 minutes on the court - contributing four assists and scoring just one point from a free throw in the final minute of the game.
Cleveland guard Kyrie Irving was strong with 21 points, eight assists and a sensational block on Dennis Schroder in the final seconds.
Schroder top scored for the Hawks with 27 points.