The 106-91 triumph, the Knicks' first victory since January 4, halted what had been their longest run of of defeats in a single season.
Dennis Smith Jr led the team with 19 points, while John Jenkins and Kadeem Allen scored 14 each.
Davis, having contributed 14 points, was ruled out of the rest of the game at half time due to a shoulder problem.
Julius Randle and Jrue Holiday scored 65 between them (33 and 32 respectively) for the Pelicans, while Russell Westbrook led the Thunder with 44.
Westbrook extended his NBA record by registering an 11th straight triple-double and became his franchise's all-time points leader.
The Orlando Magic claimed a fifth successive victory as the Charlotte Hornets were beaten 127-89 at the Amway Center.
Terrence Ross, one of six Magic players to hit double figures, finished with a game-high 21 points.