Newcastle thrashed Spaniards Cetransa El Salvador 97-0 to join Worcester, Bath and Sale in securing a home European Challenge Cup quarter-final.
The Falcons ran in 15 tries, with Ollie Phillips grabbing four, to book a home tie against French side Castres.
Worcester, who trounced Bucuresti 46-0 on Saturday, will host Montpellier - who drew 14-14 with Sale - while the Sharks take on Brive at Edgeley Park.
The fourth tie will be an all-English affair with Bath entertaining Leeds.
Leeds were left sweating on their place after their 13-3 defeat at Castres last Thursday, but they finished as one of three best runners-up.
The ties will be played on the weekend of 4/5/6 April.