He later apologised to Rylance for the rant, explaining he would always stick up for family.
Stallone himself was in more magnanimous mood, posting a picture of himself on Instagram in his black and blue Oscar tuxedo winking at the camera, fist clenched in defiance.
The 69-year-old was last Oscar-nominated 39 years ago as best lead actor and writer for Rocky.
A host of celebs rushed to ally themselves with Team Sly, including British media personality Piers Morgan, US actress Mia Farrow and Arnold Schwarzenegger, Stallone's co-star in action franchise The Expendables.
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Rylance, 56, was asked backstage how it felt to have outpunched Stallone but said he didn't take awards too seriously.
"I don't know, people come up and say things about competing as actors and I know it's necessary to make a show out of it," he told reporters."I feel more I am a spokesman than someone better than the (other) nominees."
- AAP