Lorde, whose real name is Ella Yelich-O’Connor, performed All Apologies, a track from the band’s 1993 final studio album In Utero, backed by Dave Grohl, Krist Novoselić and Pat Smear on the night.
“She’s passionate, so she’s perfect for the job,” said Novoselić, who like Lorde, has Croatian ancestry himself.
Lorde was not the only female vocalist on the night, with St Vincent, Kim Gordon and Joan Jett also singing with the trio.
“So honoured and happy I got to help celebrate Nirvana’s Rock and Roll Hall of Fame induction tonight. True [expletive] rock stars, all forever,” Lorde tweeted after the gig.