The rock act appeared on the station's breakfast show to promote the campaign to get their track to Christmas number one. It is currently winning in a chart battle with X Factor victor Joe McElderry.
However, during the crescendo of their performance, frontman Zach De La Rocha screamed the lyrics, "F**k you, I won't do what you tell" repeatedly.
Hosts Nicky Campbell and Shelagh Fogarty apologised afterwards, explaining that they had asked the band to censor the track.
Earlier, the group thanked fans who had organised the festive chart campaign, arguing that it had tapped into a "silent majority" of "real fans of music".
"This has been a real grassroots campaign from real fans of music, which has tapped into the silent majority who are tired of being spoon-fed one schmaltzy ballad after another - they want to take back their own charts," said guitarist Tom Morello. "We are honoured they have chosen our song to be the rebel anthem to topple the X Factor monopoly."
He also disputed claims that their track reaching number one would benefit Simon Cowell as it is released by Sony Records.
"People are not buying 'Killing In The Name' to protest at a record being released by a big record company," said Morello. "We wrote the song in a small industrial slum in Los Angeles. The X Factor song was produced by a cabal of overpaid songwriters to shove that schmaltzy business down your throat."
He also explained that the "windfall" of earnings they would make from the campaign would be donated to homeless charity Shelter.