The two actors are said to have fought it out for a 67-million-year-old Tyrannosaurus bataar fossil in an auction which was broadcast live to Beverly Hills from New York's IM Chait Gallery.
A source told National Enquirer magazine: "The auction was very heated. Both actors just went up and up and up." Bidding for the 32-inch-long skull began at $100,000 but Cage beat DiCaprio eventually with a final bid of $276,000.
The 'Ghost Rider' star already owns a human skull which he has nicknamed Vince.