Phoenix, 45, won the prize for playing a new take on the Joker, the villain Ledger memorably portrayed in 2008's The Dark Knight.
Phoenix also won a Golden Globe and Critics' Choice Award for his performance this season.
Ledger won an Oscar for the role in 2009, more than a year after he died of a drug overdose at age 28.
"I am standing here on the shoulders of my favorite actor, Heath Ledger," Phoenix said Sunday.
He also paid tribute to his fellow nominee, Once Upon a Time in Hollywood actor Leonardo DiCaprio.
"Leo, you've been an inspiration for over 25 years to me and so many people. I thank you very, very much," Phoenix said, acknowledging he has lost many parts to DiCaprio, 45, throughout his career.
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