Collison, who filled in for injured Chris Paul, also had 11 assists in the victory, which ended Atlanta's seven-game winning streak.
Thornton was 9-of-16 from the field in just over 26 minutes off the bench.
"Marcus Thornton was definitely the story of the game. We really didn't have an answer for him," said Hawks Coach Mike Woodson. "Their guard play really helped them to get over the hump."
Peja Stojakovic added 17 points for the Hornets and David West contributed 12 points and 10 rebounds.
Atlanta had 20 points from Jamal Crawford and 17 from Marvin Williams.
The Hornets, playing their third game under new head Coach Jeff Bower, led 49-42 at halftime and managed to fend off challenges by Atlanta in the second half.
The Hawks trailed 78-71 with 7 minutes remaining in the game but New Orleans notched a pair of 3-pointers in the next 2 1/2 minutes and hit four free throws in the stretch to close out the victory.