The bonus-point victory moves the Falcons into second place in Pool Three of the Challenge Cup on 11 points, but they need to beat leaders Brive at home and Italian minnows Petrarca away in the final two rounds to have any say in the cup playoffs.
Wallaby legend Matt Burke opened the scoring with a try in the 18th minute and backrower Eni Gesinde's effort five minutes later gave the Falcons a 14-0 lead they were never going to relinquish.
A yellow card to hooker Tony Testa did not help the visitors and Burke's second try on the half-hour mark handed Newcastle a 21-0 lead at half-time.
Winger Tom May supplied the bonus-point try and Falcons director of rugby John Fletcher cleared his bench with the game won.
Backrower Brent Wilson completed the rout with a try in the dying minutes and fly-half Toby Flood retained his perfect record with a fifth conversion.