Ramon Sessions had 12 points and five assists for the Cavaliers (3-1).
Dirk Nowitzki's 13 points paced the Mavericks (1-3), who used 14 players.
Cavaliers coach Byron Scott got 13 players into the game as he tries different lineups while the team adjusts following the offseason departure of LeBron James.
Mavs coach Rick Carlisle was back on the bench three days after collapsing at a team practice. He was hospitalized following a fainting spell during Friday's team workout and missed Saturday night's outdoor game against Phoenix in California.
The 50-year-old Carlisle rested over the weekend, and was back for Monday's shootaround. He insisted he experienced no ill effects from the episode.
Leon Powe's baseline drive and layup with 2:56 remaining gave Cleveland the lead for good at 79-77. Powe's fastbreak layup with 56.6 seconds left extended the Cavaliers' lead to 84-79.
The teams were even at 62 entering the final quarter after Dallas held a 46-45 halftime lead.
The Cavaliers were without G Mo Williams (right groin) and Cs Loren Woods (left Achilles tendinitis) and Anderson Varejao (recently returned from excused absence). All three are working out in Cleveland. ... Dallas G Rodrigue Beaubois is back in a walking boot after experiencing swelling in his surgically repaired right foot over the weekend. Beaubois fractured the fifth metatarsal during the offseason, but had shown progress in his rehab and had been allowed to shed the boot about two weeks ago. Carlisle said the situation is only a minor setback, although he doesn't know if Beaubois will be ready for the regular-season opener on Oct. 27. ... Longtime Cavs radio play-by-play announcer Joe Tait remained hospitalized in Houston with pneumonia. The team said Tait experienced discomfort and chest pains during and after Cleveland's game at Houston on Sunday night. He was hospitalized overnight for observation and tests.