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.