So why didn't Stallone win the supporting actor Oscar on Sunday?
It could be a case where the academy's small, serious East Coast contingent scored a win over its Hollywood counterparts.
Rylance also served as the first artistic director of Shakespeare's Globe in London, from 1995 to 2005.
In other words, the 56-year-old actor has an impeccable résumé that appeals to those serious about their craft.
Stallone, meanwhile, is seen more as a movie star than an actor's actor. Academy members often expressed reservations about voting for him this year, saying he was essentially playing the same character in yet another "Rocky" movie. He did it quite well. But the degree of difficulty wasn't high.
Rylance meanwhile used restraint and silence to great effect in his portrayal of a Soviet mole in "Bridge of Spies," taking a character that could have been unsympathetic and turning it into one of the movie year's most memorable movie creations.
"I try to avoid judging the characters I play, even an out-and-out bad guy like Richard III," Rylance told The Times in an October interview. "I just try to figure out what they need and play that. I don't know exactly what he was doing. I didn't set out to make him charming.
"I think being charming was the last thing he'd be concerned about."
Backstage after accepting the Oscar, Rylance said he didn't take the win too seriously, noting the quality of his fellow nominees.
"I feel more like I'm a spokesman when I win," Rylance said.
Not that he wasn't savoring the victory and the glamour of a trip from New York to Hollywood for the Oscars.
"It's very exciting. You feel very grand being driven from a small theater in Brooklyn in a black car and then flown in this incredibly powerful jet with big windows. It's a trippy experience," he said. "And then you arrive here and have so many people you don't know say nice things to you. "I quite recommend it."
Times staff writers Jessica Gelt and Rebecca Keegan contributed to this report.