The victory allowed the Pelicans (46-34) to move within a half-game of Utah (46-33) for fourth place in the Western Conference with just two games remaining.
Golden State (57-23), which is locked into the second spot in the West, lost a second straight.
The Pelicans trailed 108-105 after a Durant 3-pointer with 6:40 to go before Moore hit two hoops and teammates Darius Miller and Nikola Mirotic buried 3-pointers in a 14-3 flurry that gave the visitors a 119-111 lead with 3:54 remaining.
Down 121-113 after an Anthony Davis basket with 3:22 left, Golden State scratched back within two on hoops by Durant, Draymond Green and Andre Iguodala, the latter a dunk with 1:01 to play.
But with a chance to tie, Durant had the ball knocked away by the much smaller Rondo with 31.3 seconds left, and Moore followed with his key hoop almost eight seconds later.
Davis had a team-high 34 points and 12 rebounds for the Pelicans, who finish the regular season at the Los Angeles Clippers on Monday and then at home against San Antonio on Wednesday.
Rondo (12 points, game-high 17 assists) also recorded a double-double while Mirotic added 28 points, Jrue Holiday 25 and Moore 15 for New Orleans.
New Orleans recorded 15 steals in the game, with Holiday getting four and Rondo two.
Durant finished with a game-high 41 points for the Warriors, who fell a half-game behind Toronto (57-22) in the battle for the second-best record in the NBA behind Houston.
Durant also had 10 rebounds while Draymond Green just missed a triple-double with 11 points, 10 rebounds and nine assists.
Quinn Cook added 21 points, Klay Thompson 18 and Kevon Looney 10 for the Warriors.
The Pelicans outshot the Warriors 56.3 percent to 54.4.
--Field Level Media
New Orleans | Golden State | |
Anthony Davis 34 | Scoring | Kevin Durant 41 |
Rajon Rondo 17 | Assists | Draymond Green 9 |
Anthony Davis 12 | Rebounds | Kevin Durant 10 |
Anthony Davis 8 | Free Throws Made | Kevin Durant 5 |
Jrue Holiday 4 | Steals | Nick Young 2 |
Anthony Davis 4 | Blocks | N/A |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
New Orleans | 126 | 56.3 | 11-27 | 17-22 | 39 | 34 | 6 | 15 | 8 |
Golden State | 120 | 54.4 | 15-33 | 7-11 | 31 | 42 | 0 | 3 | 17 |