Davis' three-pointer gave LA an 86-79 lead with 6:52 left, keying a late Clippers spurt after the Mavericks' Jason Terry hit a two-point jumper, knotting the score at 79 with 8:30 remaining.
Al Thornton scored 17 points, Cuttino Mobley and rookie Eric Gordon had 11 points apiece, while both Chris Kaman and Paul Davis had 10 each for the Clippers, who came into the game at 0-6, their worst start since the 1998-99 squad opened with a 0-17 mark.
Dallas was led by Dirk Nowitzki's game-high 33 points. He also had seven rebounds.
Gerald Green had 13 points and 12 rebounds and Jerry Stackhouse scored 10 points, but no other player scored in double figures for the Mavericks, who won their four games against the Clippers last season.