Anthony Davis, recovering from spraining his elbow two weeks ago, hinted he may soon be back to his best as he finished on 32 points, 15 rebounds and seven assists.
Wesley Johnson drained a right-wing jumper to power the Pelicans into the lead with just four minutes remaining, with Chicago unable to claw their way back.
Dennis Schroder recorded a season-high 28 points on 11-of-19 shooting to help the Oklahoma City Thunder overcome the Cleveland Cavaliers 95-86.
Oklahoma held off a late run by the Cavs in the fourth quarter to win their sixth straight game.
The Los Angeles Lakers also held their nerve to edge the Minnesota Timberwolves 114-110, with LeBron James leading the way on 24 points.
Derrick Rose made his seventh triple to bring Minnesota to within one point of the Lakers with just a minute remaining, but it was not enough and the Lakers pulled ahead to seal the win.
The Miami Heat beat the San Antonio Spurs for the first time in four years, claiming a 95-88 victory.
Hassan Whiteside took 18 points before half-time, eventually finishing on 29 points, 20 rebounds and an NBA season-high nine blocks.
Meanwhile, the Detroit Pistons snapped a five-game losing streak to beat the Orlando Magic 103-96, while the Philadelphia 76ers took their first road victory of the season with a 100-94 win over the Indiana Pacers.
Kawhi Leonard impressed on his return from an ankle injury, making a crucial three-pointer in the fourth period to lift the Toronto Raptors to a 114-105 victory over the Sacramento Kings.
Elsewhere, the New York Knicks beat the Atlanta Hawks 112-107, the Utah Jazz defeated the Dallas Mavericks 117-102 and the Memphis Grizzlies took an 89-87 win over the Denver Nuggets.