The 24-year-old Davis passed David West on the franchise list and has 8,702 points. He made 17 of 34 shots and had 10 rebounds.
E'Twaun Moore added 26 points for the Pelicans.
New Orleans had lost two straight since All-Star DeMarcus Cousins was lost for the season with a left Achilles tendon rupture. They righted the ship by shooting 51 percent from the field against the Thunder.
Oklahoma City’s Russell Westbrook had 16 points, 14 assists and 10 rebounds for his 16th triple-double of the season. Steven Adams had 23 points and 12 rebounds for the Thunder, who lost their third straight after an eight-game winning streak.
Westbrook approached a triple-double in the first half with nine points, nine assists and seven rebounds to help the Thunder take a 58-54 lead at the break.
The Pelicans seized momentum early in the third quarter. New Orleans led 97-89 in the fourth when Westbrook checked back in after a rest.
Westbrook made a 3-pointer with just under two minutes remaining to cut the lead to seven, but Davis hit a 3-pointer at the other end, then made another shortly after that to put the game out of reach.