Perkins was thrown out of the game and given two technical fouls late in the second quarter of Wednesday's game after reacting to a foul call.
The second technical foul gave Perkins seven playoff technicals, which calls for an automatic one-game suspension.
However, the NBA Thursday pulled back the second technical, allowing Perkins to play Friday. There was no explanation given by the league for the change.
Boston leads the best-of-seven series 3-2 but has lost the last two games.
The NBA also upgraded Paul Pierce's foul on J.J. Redick in the fourth quarter to a Flagrant 1.