The Nuggets player is only the fourth player to score 50 points in an NBA season-opener
Davis connected on 17 of 34 shots from the field and 16 of 17 free throws. He also pulled down 16 rebounds, blocked four shots and had seven steals.
But his eighth career game of 40 points or more -- nine short of his career high of 50 -- wasn't enough.
"When you play against a great player, you have a problem you need to answer: are you going to shut him down and create problems elsewhere or are you going to let him get his and hope nobody else goes off?" Denver coach Mike Malone said. "Anthony Davis, give him credit, got 50 points.
"The Denver Nuggets got the win, and that's the most important thing."
The only other players to score 50 points in a season-opener are Wilt Chamberlain, Elgin Baylor and Chicago Bulls icon Michael Jordan.
"It's tough," Davis said. "We had some chances, but we gave them too many easy looks at the beginning of the game. It would have been more satisfying if we had won, but the way I played, I'm going to have to bring, probably not 50 every night, but get somewhere along those lines every game to give ourselves a chance to win. That's the bottom line."
Denver's Bosnian center Jusuf Nurkic produced 23 points and nine rebounds and Will Barton added 22 points as the Nuggets overcame not just Anthony, but their own 25 turnovers.
New Orleans closed within six points three times in the fourth quarter, but Denver responded each time.
Kenneth Faried was a key stopper, drawing two charges and grabbing a tough offensive rebound for a follow-up basket.
He also assisted on a three-point play by Wilson Chandler that put Denver up 94-85 with 7:09 to play.
Davis cut the deficit to 100-98 with two foul shots and a dunk with 2:32 remaining.
But after Barton was fouled on a drive and hit both free throws it was 102-98.
Davis then came up with his seventh steal of the contest, picking the pocket of Denver's Congolese point guard Emmanuel Mudiay and racing in for a layup that made it 102-100.
Fouled on a jump shot, Mudiay made one of two from the free-throw line. He added four more free throws in the final 12.9 seconds left to seal the game.