Rylance, 56, triumphed over Sylvester Stallone ('Creed'), who had to return empty handed despite winning the Golden Globes and Bafta.
"I've always adored stories, hearing them, seeing them... So for me, to get a chance to work with one of the greatest storytellers of our times, Steven Spielberg, has been such an honour. I am so pleased our film has been nominated so many times. It's a wonderful time to be an actor right now," Rylance said while accepting his Oscar trophy.
Critics loved Rylance's stoic portrayal of Abel, who is apprehended and tried for espionage in the US before being returned to Soviet Russia in a spy exchange.
Initially wary of New York lawyer James Donovan, who is defending him, Abel and Donovan develop a trust despite the hostile atmosphere.
A three-time Tony winner, Rylance has a long stage, TV and film career. He appeared in theatrical performances of "Much Ado About Nothing", "Twelfth Night" and "Boeing Boeing" among many others.
His notable films include "Prospero's Books", "Angels and Insects", "Intimacy", "The Other Boleyn Girl" and "Anonymous".
Other than "Bridge of Spies", Rylance also won acclaim for playing Thomas Cromwell in the 2015 BBC Two miniseries "Wolf Hall."
In his speech Rylance acknowledged fellow nominees in the supporting actor categories including Stallone ('Creed') Christian Bale ('The Big Short'), Tom Hardy ('The Revenant') and Mark Ruffalo ('Spotlight').
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