The Hawks broke the game open with a 23-4 run during the last half of the third quarter, while New Orleans was in the midst of missing 12 straight shots.
Emeka Okafor scored 13 points for New Orleans, which was as close as 53-48 on Jarrett Jack's free throws with 5:44 to go in the third before Atlanta took over.
Jack finished with 10 points in the Hornets' 16th loss in 18 games.
The Hornets, who have lost 10 times by single digits, have been competitive in most of their games and had hoped they were turning the corner after a lopsided victory over Orlando on Friday night, which snapped a nine-game skid. Instead, they responded with one of their worst games of the season, shooting only 37.5 percent (27 of 72).
The Hornets shot 5 of 19 in the first quarter and 5 of 20 in the third. They went from 7:06 of the third quarter to 9:35 of the fourth without hitting a field goal (0 for 12) and turned the ball over six times during that stretch.
The Hawks shot 44 percent (36 of 82) and went 12 of 23 on 3-pointers, with Teague hitting all four he attempted. Williams was 3 of 4 from long range. Atlanta also outrebounded New Orleans 42-36.
Joe Johnson and Ivan Johnson each scored nine points for the Hawks.
Teague left Atlanta's previous game at Detroit on Friday with a sprained left ankle, but he returned to the starting lineup Sunday and had an immediate effect on the game.
Atlanta raced to a 12-2 lead with Williams and Teague each hitting 3s and Teague adding a 16-foot jumper. Teague then hit back-to-back 3s on his way to 11 first-quarter points and the Hawks took a 21-point lead barely 9 minutes into the game when Kirk Hinrich's layup made it 27-6.
The Hornets clawed back into the game with an 11-0 run in the second quarter during which Okafor scored five points and capped the surge with a three-point play on an inside basket to make it 33-26.
Williams' second 3 of the game interrupted the spurt before Okafor scored inside and Gustavo Ayon hit a reverse layup to cut it to 36-30. Atlanta then built its lead back to double digits, closing out the half with a 6-1 mini-run capped by Johnson's driving floater from the lane to make it 46-35.
Notes: Greivis Vasquez tied a career high with eight assists. ... During New Orleans' 11-0 run in the second quarter, Green hit a jumper at the shot-clock buzzer that was initially ruled good and overturned on replay. ... The Hornets' 21-point deficit in the first quarter was at that point the largest deficit for New Orleans this season until it got worse in the second half. ... The Hornets entered the game having played the toughest schedule in the NBA through their first 19 games when measured by their opponents' combined winning percentage of .587. ... New Orleans and Atlanta meet only once in this lockout-shortened season. ... Atlanta is 3-1 on its five-game road trip, which concludes Monday night at Toronto. ... The Hornets had not lost a game by more than 16 points (at Sacramento).