The Knicks made 15 free throws in the final period and produced 40 points and withstood 32 points and 13 assists from New Orleans point guard Chris Paul.
Big man David Lee had 28 points and eight rebounds for New York (1-3), which used a 10-2 run midway through the fourth to turn a two-point lead into a 102-92 advantage with 4:09 left.
Harrington enjoyed his second straight strong performance after coming off the bench to score 42 points in the Knicks’ loss to the Philadelphia 76ers on Saturday.
New York had dropped successive games in overtime before finally breaking through against the Hornets.
“We’ve been finishing games strong — we just haven’t had that good start that we need to sustain runs and things like that,” Knicks guard Larry Hughes told reporters after delivering 20 points in his first start of the year.
“We can make runs at anytime, so getting off to that good start helps.”
New York started the game with a 16-6 run and led 58-52 at halftime. The Hornets snatched control of the game in the third where Paul tallied 11 points before finishing the night with season highs in points and assists.
Center Emeka Okafor, acquired in the off-season, had 24 points and 10 rebounds for his first double-double with New Orleans while forward David West had 21.
“If I knew what happened tonight I’d tell you,” Paul said. “We watched film and knew coming into the game that these guys play five guys around the 3-point line and have great shooters.
“At the end of the day we have to stop the guys that are in front of us.”