J.R. Smith had 15 points and James Jones added 13 for the Cavaliers, who swept Atlanta in the Eastern Conference finals last season. LeBron James had eight points and seven rebounds in 22 minutes for Cleveland.
Al Horford scored 15 points and Kent Bazemore had 12 for the Hawks.
Cleveland played without Kyrie Irving (knee) and Kevin Love (shoulder) and Tristan Thompson is not playing while negotiating a new contract.
Atlanta was missing Thabo Sefolosha, who broke his leg while being arrested by New York City police in April. Sefolosha is on trial in New York for his involvement in a fight outside a nightclub. He is expected to be ready for the season opener.
Love has been cleared to participate in 3-on-3 drills starting Saturday. He is expected to play Monday against Memphis.
Atlanta plays New Orleans on Friday in Jacksonville, Florida. Cleveland plays at Philadelphia on Thursday.