Yauch used the group's growing fame to attract awareness for Tibetan Buddhists. He founded the Milarepa Fund to promote activism for Tibet in defense of what the nonprofit considered China's occupational government.
In 1996, Yauch and Milarepa produced a hugely popular benefit concert for Tibet in San Francisco, which was followed by more international concerts over the next decade.
"He was a goofball and behind a lot of their prankiness, but if you wanted to talk to him about what was going on in the world and social issues and everything, you got a totally different guy," said Rick Krim, executive vice president of music and talent relations at Vh1.
Introducing the group at the Rock Hall, Public Enemy rapper Chuck D said the Beastie Boys "broke the mold."
"The Beastie Boys are indeed three bad brothers who made history," Chuck D said. "They brought a whole new look to rap and hip-hop. They proved that rap could come from any street — not just a few."
Yauch also went under the pseudonym Nathanial Hornblower when working as a filmmaker. He directed numerous videos for the group, as well as the 2006 concert film "Awesome: I F-----' Shot That!" (shot entirely by fans given cameras) and the basketball documentary, "Gunnin' for that (No.) 1 Spot."
In 2008, he co-founded the noted independent film distribution company Osciolloscope Laboratories, named after his New York studio.
Yauch is survived by his wife, Dechen Wangdu, and his daughter, Tenzin Losel Yauch.
Yauch's illness, about which he first expressed hope that it was "very treatable," forced the group to cancel shows and delayed the release of their last album, "Hot Sauce Committee, Pt. 2." He hadn't performed in public since 2009.
But the enduring popularity of the Beastie Boys across some 28 years is one of the steadiest paths of success in pop music — a time remarkable for the constant, warm camaraderie between Yauch, Horovitz and Diamond.
"They are truly rock's most realized group — not hip-hop but all music, really," wrote Questlove, the drummer for the Roots, who toured with the Beastie Boys. "I mean, did we really expect the most thoughtful, mature, considerate act in music to be the same brats who gave us 'Licensed To Ill'?"
AP Music Writer Nekesa Mumbi Moody and AP writer Mesfin Fekadu contributed to this report.