The song is actually sung by Josh Homme, the frontman of the band Queens of the Stone Age.
While Jack Black is a talented musician and actor, he's known for his comedic roles and work in bands like Tenacious D. He doesn't have any official recording or performance history with Queens of the Stone Age.
The misunderstanding may come from the fact that Jack Black is a huge fan of Queens of the Stone Age and often expresses his admiration for their music. He's even been known to cover "Master Exploder" in live performances with Tenacious D.