Davis was in the game when the first half ended, but kept his left arm still as he walked to the locker room shortly after fouling Nerlens Noel on an attempted shot block with his left hand in the final second of the second quarter, The Associated Press reported.
When the second half began, the Pelicans announced that Davis was out of the remainder of the game with a left shoulder injury, putting his availability for the weekend's All-Star Game in doubt.
Russell Westbrook increased his record triple-double streak to 11 games with 44 points, 14 rebounds and 11 assists. But he missed a late three-point attempt when the Thunder trailed by five just inside the final minute of the game. New Orleans rebounded and held on from there.
Jrue Holiday had 32 points and seven assists, none more timely than his driving feed to Randle in the paint with 1:30 to go.
Paul George scored 28 points for Oklahoma City, which had its four-game winning streak snapped.
Davis was in the starting lineup and played 16 minutes during the first half. He scored 14 points, grabbed four rebounds, assisted on two baskets and blocked a shot. His performance helped New Orleans take a 66-63 lead into halftime.
Davis did not emerge from the locker room to start the second half.
Coming off a listless, 30-point loss to Orlando two nights earlier in which Davis scored just three points on 1-of-9 shooting, the Pelicans bounced back with a far superior showing against a team with the third-best record in the Western Conference.
The Pelicans led for most of the game and by as many as 17 on Randle's free throws with five minutes left in the third quarter.
The Thunder pulled as close as 121-118 with 2:52 left, when George hit a straight-on three, hollering and pounding his chest after the shot went down.
But the Pelicans didn't fold thanks to Randle, who responded to George's clutch three by tipping in Kenrich Williams' missed three-pointer.