Dirk Nowitzki hit a 3-pointer to bring Dallas within 95-92 with 5 seconds remaining but Belinelli wrapped up what was only the ninth win of the season for the Hornets.
The victory over the defending NBA champions was the first of the season for New Orleans against a division opponent.
New Orleans led by 12 early in the fourth quarter before Dallas cut its deficit to two with less than 5 minutes left.
Dallas has lost four in a row and five out of six. Roddy Beaubois scored 25 points off the bench for the Mavericks.
Nowitzki, who suffered a sore back during a loss to Memphis Wednesday and played just 10 minutes in that game, wound up with 19 points.