Howard was 9-of-14 from the field and grabbed seven rebounds. Dirk Nowitzki scored 14 points and led Dallas with 11 rebounds, and Jose Barea also had 14 points.
Chris Paul led the Hornets with 16 points and 11 assists, and Rasual Butler added 13 points.
Mavericks guard Jason Terry was given the night off and did not dress for the game.
New Orleans started the fourth quarter on a 26-8 run to narrow a 19-point Dallas lead to 93-92 with 3:52 remaining before Dallas went on a late 9-1 spurt to seal the win.
The Hornets struggled from the line, missing their first nine free throw attempts and finishing the game 17-of-29.
The Mavericks shot 71 percent in the third quarter on 12-of-17 shooting and led 85-66 heading into the final period.
The Hornets used a 20-4 run in the second quarter to erase a 16-point first-quarter deficit and tie the game at 52 at the half. Harris led Dallas with 12 first-half points and Howard added 10.
Dallas scored the first 14 points of the game and led 36-20 at the end of the first quarter.
The Mavericks play their final preseason game against Chicago on Tuesday before they open the season at Cleveland on Oct. 31. The Hornets have two exhibition games left before starting the regular season against Sacramento on Oct. 31.