Introducing the track, Rivers told the crowd: ''We're gonna cover a song from Dave Grohl's old band to tide you over until the main course in a few minutes.''
Dave and his bandmates then returned the compliment, by doing a rendition of Weezer's 1996 track 'Big Me', and he admitted he really misses playing 'Lithium'.
He said: ''Tonight I'm gonna dedicate this one to Weezer.
''I was backstage and I heard Weezer play the 'Lithium' song. I gotta be honest, I cried a little bit. I did!
''I miss playing that song. I miss it, so I'm happy to hear Weezer play it again. So this one goes out to the sweet Weezer.''
Hearing and playing Nirvana songs is particularly emotional for Dave after frontman Kurt Cobain's death from suicide, aged just 27, in April, 1994.
Last year, the 'Smells Like Teen Spirit' drummer performed 'In Bloom' for the second only time since Kurt's passing.
He took to the stage with Trombone Shorty at Voodoo Threauxdown Festival in Los Angeles for a rendition of the track from the grunge band's seminal 1991 LP 'Nevermind'.
The last time he played the song was when the band were inducted into the Rock and Roll Hall of Fame in 2014.
The likes of Lorde, Joan Jett, Kim Gordon and St. Vincent joined forces for the special performance.
Speaking previously on why he struggles playing Nirvana songs live since his late bandmate's passing, Dave explained: ''For years I couldn't even listen to any music, let alone a Nirvana song.
''When Kurt died, every time the radio came on, it broke my heart.
''I don't put Nirvana records on, no. Although they are always on somewhere. I get in the car, they're on. I go into a shop, they're on. For me, it's so personal.
''I remember everything about those records; I remember the shorts I was wearing when we recorded them or that it snowed that day. Still, I go back and find new meanings to Kurt's lyrics.''
What's new in the music world this week?
Watch three incredible live performances from Discovr.TV.
Don't miss the K-pop titans' return to Europe.
Listen to Alex Bayly performing 'Animal'.
Two weeks ahead of Independent Venue Week, Dry Cleaning made 'Britain's Best Small Venue 2015' (NME) the second port of call on their 2020 tour.
'Leave Home' was released on this day (January 10th) in 1977.
For their last gig of the year, The Libertines came back to their adopted hometown of Margate to finish off their latest tour.
In a new clip from the forthcoming official Kurt Cobain documentary, we discover the birth...
Kurt Cobain was trapped in a troubled homelife as a child with his parents having...
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Underneath the famous Muppet Theatre, oil has been discovered. Tex Richman, an oilman, finds out...