The Hawks left the court that night with a 117-111 victory, but commissioner David Stern struck it from the books after the home team's stat crew mistakenly ruled that O'Neal, then playing for Miami, had fouled out with less than a minute to go in overtime.
O'Neal has since been traded to Phoenix, but the NBA said Monday that both teams can fill out any openings on their 12-man active roster with players acquired since the disputed game.
That means the Heat can dress Marion and Marcus Banks, who came from the Suns in the Shaq deal. Likewise, the Hawks will be able to use Bibby, who was picked up from Sacramento just ahead of the trade deadline.
The Hawks, who gave up four players for Bibby, have nine active players still around from the disputed game. Also eligible to be added for the replay are Josh Childress, Jeremy Richardson and Speedy Claxton.
Miami will have the ball when the game resumes, trailing 114-111. After the replay is completed, the teams will get a 15-minute break, then return to the court for their regularly scheduled contest at Philips Arena.
The night is vitally important to the Hawks, who are battling for a playoff spot in the Eastern Conference and can hardly afford to squander an apparent win against hapless Miami, which has the NBA's worst record (11-46).
Stern also fined the Hawks $50,000, ruling they were "grossly negligent" in failing to address the mistake.
Miami's protest was the first granted by the NBA since December 1982, when then-NBA commissioner Larry O'Brien upheld a request for a replay by the San Antonio Spurs after their 137-132 double-overtime loss to the Los Angeles Lakers the previous month.
The Spurs and Lakers finally finished the game in April 1983, with San Antonio winning 117-114.