Evans shot 14-of-26 from the field and 12-of-16 from the free-throw line for New Orleans, which had lost eight straight games. Luke Babbitt donated 12 points off the bench, while Darius Miller and Alexis Ajinca had 10 points apiece.
Kevin Durant and Serge Ibaka scored 25 and 22 points, respectively, in the setback, while the other three Thunder starters combined for just eight points on 3-for-17 shooting. With the playoffs approaching, Russell Westbrook took the game off to rest his surgically repaired knee.
Oklahoma City has now blown two opportunities to clinch the No. 2 seed in the Western Conference following Sunday's loss to Indiana. The Thunder need a win Wednesday against Detroit or a Clippers' loss in either of their final two games to lock up the two seed.
Despite playing without six of its seven top scorers, New Orleans found a way to take down the playoff-bound Thunder behind Evans, who nearly matched Oklahoma City's fourth quarter total by himself. The Pelicans outscored the Thunder, 31-20, in the fourth, with Evans netting 17.
New Orleans led 70-69 through three quarters, but it was tied at 77 after Durant's short jumper at 7:34.
Miller's 3-ball restored the lead for the home team. Anthony Morrow followed with a triple of his own and after the teams traded baskets over the next few possessions, Evans hit from deep for a 90-82 margin with just over four minutes remaining.
Oklahoma City had one final push, with Durant's 3-pointer with 2:08 to play pulling it within seven, but Babbitt countered with a three at the other end.
Earlier, Pelicans guard Austin Rivers and Thunder forward Nick Collison were both ejected for their roles in an altercation midway through the second quarter.
New Orleans led 23-21 after the first quarter, but trailed 46-45 at intermission.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys