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Marco Belinelli had 16 points to lead New Orleans, which rallied from a 55-40 halftime deficit to cut the lead to 97-96 with just under three minutes remaining.
Hansbrough, who missed all but 29 games as a rookie last season because of issues with his inner ear and vertigo, scored 11 points in the third quarter and showed much of the aggressiveness and physical inside play that made him the No. 13 overall selection by Indiana in the 2009 draft.
Hansbrough, the 2008 ACC Player of the Year for North Carolina, made 7 of 8 free throws and had five rebounds.
The Pacers (2-3) also continued to use the preseason to work newcomers into the starting lineup after an offseason of change.
Swingman Mike Dunleavy, starting for the fourth time in five preseason games after starting 15 games last season and playing just 18 the season before because of knee problems, scored 13 points.
Indiana center Roy Hibbert added 15 points and five rebounds, and power forward Josh McRoberts led Indiana with eight rebounds to go with eight points.
Nick Collison, starting at point guard after being acquired by Indiana in an off-season trade, scored 16 points and also had five assists with seven turnovers.
Forward Trevor Ariza scored 15 point for the Hornets (1-3) and forward Jason Smith had 14 points and a team-high nine rebounds.
Guard Chris Paul had 12 points and eight assists for New Orleans, which outscored the Pacers 37-25 in the third quarter.
But after the Hornets cut the lead to one point twice in the final three minutes -- the final time on a pair of free throws by Willie Green with 38.1 seconds remaining - James Posey converted two free throws with 11.4 seconds remaining.
Belinelli missed from 27 feet on the right side, and Smith stepped out of bounds with the rebound to secure a second consecutive preseason victory for Indiana.
Pacers forward Danny Granger sprained an ankle in the second quarter and did not return. He finished with eight points, and Pacers reserve point guard T.J. Ford left the game in the second half with a sore right hamstring and did not return.