We broke the story -- EMTs responded to a call at Tom's home Sunday night for a person who was unconscious, not breathing and in full cardiac arrest -- he was taken to UCLA Santa Monica Hospital, where he was immediately put on life support.

Dimitriades says Petty died at 8:40 PM PT at UCLA surrounded by friends, family and his bandmates.

After learning Tom had no brain activity, his family chose to take him off life support.

Tom hit it big in 1978 with his band, the Heartbreakers ... which scored hits with "Don't Do Me Like That" and "Here Comes My Girl" to name just a few.

Tom also wrote and recorded "Stop Draggin' My Heart Around" with Stevie Nicks in 1981.

Later in the '80s he recorded with The Traveling Wilburys -- a legendary lineup comprised of Bob Dylan, George Harrison, Roy Orbison and Jeff Lynne -- and made a big hit, "Handle with Care."

And Tom recorded solo and had the smash hit, "Free Fallin'."

He was inducted into the Rock & Roll Hall of Fame in 2002, and has remained a huge touring draw. He just wrapped up his 40th anniversary tour last week at the Hollywood Bowl.

He was 66.

RIP