"Apparently one in three Americans actually watched that performance, so if we're lucky one or three Americans might watch this YouTube video."
Saturday marked 50 years since the legendary group first appeared on The Ed Sullivan Show, shortly after holding an historic press conference on John F Kennedy Airport's central terminal.
Arctic Monkeys performed just two songs from their 2006 debut album, Whatever People Say I Am, That's What I'm Not: Dancing Shoes and I Bet You Look Good On The Dancefloor.
The quartet played 20 songs in total after opening their energetic set with Do I Wanna Know? from their fifth and most recent album, AM. Other tracks to make the cut included Fluorescent Adolescent, Brianstorm and Don't Sit Down 'Cause I've Moved Your Chair.
Miles Kane, from Turner's side project supergroup, The Last Shadow Puppets, joined the band for 505.
Arctic Monkeys had played Madison Square Garden twice before in 2012, but in a support slot for US rock group The Black Keys.
They have also covered The Beatles in the past - at the opening ceremony of the 2012 London Olympics, when they played Come Together as part of a musical tribute to British pop.
- Independent