The Lakers won 150-145 with 36 points and 16 rebounds from Davis, while James added 26 points and 10 assists.
Indiana scored 46 points in the final quarter but the Lakers hit 10 in the last minute for a third successive win.
"We allowed them to score 145 so it was terrible defensively but we can do what we want offensively," said Davis.
"But we've got to defend, especially when we've got a team [in trouble] like that. We don't need to give them life, but at this point in the season, a win is a win."
The Lakers, who start a run of six away games on Tuesday, are ninth in the Western Conference and have 11 matches remaining in the 82-game regular season. The top six qualify for the end-of season play-offs, with positions seven to 10 moving into the play-in tournament.
The Pacers are sixth in the Eastern Conference and have 10 games to play.