Williams has a sprained right wrist, which he suffered in Game 2 and kept him sidelined for Game 3. Moon strained a lower abdominal muscle during the second quarter Game 3, plus is dealing with a sore groin.
The Heat made the decision to rule Moon out Monday morning, but the Hawks were hopeful that Williams' wrist -- which had improved a bit, thanks to near round-the-clock treatment -- would loosen enough for him to play.
It didn't, meaning Atlanta placed Mo Evans in the starting lineup for the second straight game.
"We've got to go with what we've got," Hawks guard Joe Johnson said. "We can't worry about what we don't have. Other guys have to step up."
The Heat entered Monday with a 2-1 lead in the series, with the Cleveland Cavaliers awaiting the eventual winner in the second round.
With Moon out, James Jones was making his fourth straight start at small forward for the Heat.
The series continues in Atlanta on Wednesday. Moon's status seems doubtful, but Hawks coach Mike Woodson said he was hopeful that two more days of rest would be enough to get Williams back.
"We'll see how he feels on Wednesday," Woodson said.