Despite being short-handed, Atlanta jumped out to a 12-point lead after one quarter Sunday. Joe Johnson finished with a game-high 28 points on 11-of-16 shooting.
"It was very important for us to get off to a good start and sustain it (because of the injuries), especially on the road," Johnson said. "I just tried to take what the defense gave me."
Johnson, a six-time All-Star at shooting guard, is playing small forward with Williams missing his third straight game. Coach Larry Drew is starting Jeff Teague and Kirk Hinrich in the backcourt along with power forward Josh Smith, and center Zaza Pachulia, with Tracy McGrady the coach's best option off the bench.
"Everything kind of happened for a reason," Johnson said. "You now have three guys that are playmakers, can handle the ball, and make things happen."
Boston (23-21) is 2/3 on an eight-game trip with the remaining games against Eastern Conference foes after the first five were against the West. The Celtics are in seventh place in the East, 2 1/2 games behind the sixth-place Hawks.
Coach Doc Rivers' team is fairly healthy, with only Jermaine O'Neal (wrist) among injured players who will eventually return this season.
The road trip, however, has taken its toll. Boston fell 120-95 at lowly Sacramento on Friday and trailed by 13 at the half of Saturday's 98-91 defeat to Denver.
The Celtics cut a 17-point deficit to two in the fourth quarter Saturday before falling.
"I told the team that they can't ease yourself into a game and then decide you want to join the war in the fourth quarter," Rivers said. "We were a different team in the fourth quarter when we played with spirit and fight."
Paul Pierce is averaging 18.8 points on 36.7 percent shooting on this trip while Rajon Rondo is averaging 12.4 assists in the five games.
Rivers attempted to find a spark Saturday by giving Marquis Daniels nearly 20 minutes for his most action since Jan. 23. Daniels had eight points.
"I like to be an energy guy if I can, I like to play good defense and make it tough for the other team, get some easy baskets," Daniels said.
Boston took two of three matchups last season against Atlanta even though Rondo missed both victories. Johnson made 6 of 30 shots for 25 total points in two meetings while Smith missed 18 of 21 shots for a total of nine points while failing to block a shot as he played in all three.