The emerging rocker previously made his US TV debut when he played a pair of tracks on 'Jimmy Kimmel Live' in March.
The new track features on the fast-rising outfit's upcoming full-length album 'Fever Dream' out 26 July via Republic Records.
In the clip, Nick Jonas takes on vocal lead as Fallon snaps on a Casio keyboard and taps out the beat on a wood block.
They performed the band's 1971 rock classic 'Won't Get Fooled Again' as never before, on classroom instruments with house band the Roots.
The Icelandic stars will also appear on 'The Tonight Show with Jimmy Fallon' (NBC) on 15 May
The Icelandic outfit's third album, 'Fever Dream', will be released through Republic Records on 26 July.
The Roots are also, famously, 'The Tonight Show's' house band as well as much-revered hip-hop pioneers.