Several Cavaliers have had the flu over the past week, including James, but Brown said the rest was planned long ago.
Kris Humphries added 12 points and nine rebounds for the Mavericks (4-1).
Dallas was leading 78-76 with 7:28 left when Humphries connected on a 20-footer to ignite a 10-0 spurt. Rookie Rodrigue Beaubois and J.J. Barea completed the run with 3-pointers on consecutive possessions.
J.J. Hickson and Andre Barrett are not with the Cavs as they complete their recovery from the flu, but both are expected to be available for Tuesday night's rematch against the Mavericks in Pittsburgh. Brown said James, O'Neal and Mo Williams will play Tuesday night.
Tim Thomas, penciled in as a top reserve for the Mavericks, also is sidelined after right knee surgery.
Woj: LeBron questionable vs. Spurs, will test ankle in pregame
Adrian Wojnarowski provides an update on LeBron James' ankle injury and how the Lakers are handling it.
Fantasy basketball trade index: Should you trade for Evan Mobley or any other quick-starting rookies?
Eric Karabell breaks down which players to deal for -- and which to trade away -- as he takes his weekly look around the NBA.
Fantasy basketball: Five low-rostered players worth picking up
André Snellings pinpoints five low-rostered players who can provide a boost to fantasy lineups.