Jeff Foster had 12 points and 13 rebounds for Indiana while Danny Granger added 11 points and eight rebounds.
David West led New Orleans (1-1) with 17 points and Hilton Armstrong added 16.
O'Brien said all summer the Pacers would push the tempo, and it didn't take long for the home fans to see what he meant. Dunleavy scored 15 points in the first quarter to help the Pacers take a 27-16 lead.
Indiana opened the second quarter on a 9-2 run and the Pacers continued to pour it on and led 55-35 at halftime.
New Orleans erased much of that deficit early in the third quarter. The Hornets went on a 13-0 run to get within 64-61, but the Pacers recovered. A 3-pointer and a layup by Troy Murphy, then a 3-pointer by Dunleavy bumped the lead back to 72-64. Indiana led 77-66 at the end of the period.
The Hornets cut Indiana's lead to 84-79 with 7:22 to go, but Andre Owens scored a basket and a three-point play to make it 89-79, and the Pacers led by at least five points the rest of the way.
The Pacers outrebounded the Hornets 60-41, though New Orleans' best rebounder, Tyson Chandler, did not play.
The Pacers played without All-Star forward Jermaine O'Neal, who was injured Monday when he collided with Shawne Williams during practice. O'Brien said the knee swelled, and O'Neal woke up sore on Wednesday morning. O'Brien considered playing him, but took him out of the lineup about an hour before game time. The injury isn't considered serious.
O'Neal tore cartilage in the same knee last season and had surgery to repair it in April.