Reggie Theus added 17 points and Glenn Rivers 13 as the Hawks rebounded from Sunday night's loss to the expansion Miami Heat.
It was the Clippers' fifth straight loss and 24th in their last 25 games. Atlanta has won four of five games since the All-Star break.
"We played with a younger squad than we usually do, but they were putting forth the effort and desire to make this team better, so they will continue to play," Clipper Coach Don Casey said. "The Hawks are a tough team with depth at every position, and they will be tough at the end of the season."
Wilkins scored eight points as the Hawks rolled to a 14-2 lead. The Clippers (11-41) closed to 22-19 on Gary Grant's jumper with 2:16 left before the Hawks stretched it to 30-23 by the end of the quarter.
The Clippers, who fell to 2-27 on the road in the opener of a five-game Eastern Conference trip, got no closer the rest of the game. The Clippers trailed, 58-47, at the half.
The Clippers were behind by 28 points at the end of the third period, 92-68, but did get within 105-94 on Reggie Williams' layup with 3:41 left in the game. The Hawks then scored the next nine points.
"I think we're four, maybe five games from where we should be," Theus said after the Hawks improved to 32-20. "But we're close to our target."
Rookie Charles Smith led the Clippers with 19 points, while Benoit Benjamin, the subject of on-going trade talk, and Williams added 17 each.
The Clippers haven't won in Atlanta since Dec. 30, 1981.
Wilkins said the Hawks met before the game to talk about the Miami loss and then came out with the intention of finishing off the Clippers early.
"That's what you've got to do with a team like that," he said. "You don't want to hang around and hang around, because a team like that can hurt you. We took the game away from them and didn't let them back in it."
Coach Mike Fratello said it was important for Atlanta, which beat the Clippers, 130-101, Jan. 30 in Los Angeles, to play a solid game Monday night.
"From the standpoint of looking at the whole season, it was really good to get this win," Fratello said. "We had a difficult time last night (against Miami), and the team really bounced back."
The Clippers shot just 40.9% from the field, meaning they have gone six straight games without breaking 50%. They're at 42.6 in the last four outings, continuing the run as one of the worst shooting teams in the league.