The Pacers were ahead by two points, 77-75, with 16 seconds left when West connected on a 13-foot jumper and iced the victory for Indiana.
Paul George helped the Pacers claim their third straight with 17 points and 12 rebounds.
George Hill (12 points) and Lance Stephenson (10) also added key points for the winners.
The Hornets, meanwhile, dropped their 11th straight.
Robin Lopez (24 points, 11 boards) and Greivis Vasquez (14) led New Orleans' scorers.