In years past, whenever there were splits between Best Picture and Best Director at the Oscars, it was very rare. Though in recent years, we've been seeing those kind of splits more frequently due to the fact that both categories have been utilizing two separate voting systems. A more important film would win Best Picture with a screenplay prize while a big technical achievement would win Best Director. I’ve looked at a lot of past Oscar races where those two awards went to the exact same film, and was able to come up with 12 instances where I think nowadays we’d see splits.
1962: To Kill a Mockingbird wins Best Picture while David Lean wins Best Director for Lawrence of Arabia.
1968: The Lion in Winter wins Best Picture while Carol Reed wins Best Director for Oliver!.
1977: Annie Hall wins Best Picture while George Lucas wins Best Director for Star Wars.
1978: Coming Home wins Best Picture while Michael Cimino wins Best Director for The Deer Hunter.
1979: Kramer vs. Kramer wins Best Picture while Francis Ford Coppola wins Best Director for Apocalypse Now.
1980: Ordinary People wins Best Picture while Martin Scorsese wins Best Director for Raging Bull.
1982: Gandhi wins Best Picture while Steven Spielberg wins Best Director for E.T. The Extra-Terrestrial.
1986: Hannah and Her Sisters wins Best Picture while Oliver Stone wins Best Director for Platoon.
1992: Howards End wins Best Picture while Clint Eastwood wins Best Director for Unforgiven.
1996: Fargo wins Best Picture while Anthony Minghella wins Best Director for The English Patient.
2001: A Beautiful Mind wins Best Picture while Peter Jackson wins Best Director for The Lord of the Rings: The Fellowship of the Ring.
2009: The Hurt Locker wins Best Picture while James Cameron wins Best Director for Avatar.
1962: To Kill a Mockingbird wins Best Picture while David Lean wins Best Director for Lawrence of Arabia.
1968: The Lion in Winter wins Best Picture while Carol Reed wins Best Director for Oliver!.
1977: Annie Hall wins Best Picture while George Lucas wins Best Director for Star Wars.
1978: Coming Home wins Best Picture while Michael Cimino wins Best Director for The Deer Hunter.
1979: Kramer vs. Kramer wins Best Picture while Francis Ford Coppola wins Best Director for Apocalypse Now.
1980: Ordinary People wins Best Picture while Martin Scorsese wins Best Director for Raging Bull.
1982: Gandhi wins Best Picture while Steven Spielberg wins Best Director for E.T. The Extra-Terrestrial.
1986: Hannah and Her Sisters wins Best Picture while Oliver Stone wins Best Director for Platoon.
1992: Howards End wins Best Picture while Clint Eastwood wins Best Director for Unforgiven.
1996: Fargo wins Best Picture while Anthony Minghella wins Best Director for The English Patient.
2001: A Beautiful Mind wins Best Picture while Peter Jackson wins Best Director for The Lord of the Rings: The Fellowship of the Ring.
2009: The Hurt Locker wins Best Picture while James Cameron wins Best Director for Avatar.