Kyle Steyn went over for two tries

Warriors controlled the majority of the match and played some free-flowing rugby to go 19-3 ahead at the break.

Johnny Matthews, Kyle Steyn and Josh McKay all touched down to give the Warriors a comfortable buffer going into the second period.

Brett Connon provided the Falcons' sole response in the opening half before Will Montgomery touched down after the interval to put the hosts back into the contest.

However, Glasgow regained control of the scoreboard with Steyn crossing the whitewash for the second time to effectively seal their passage into the last-eight, despite Joel Hodgson's consolation score for Newcastle.

Warriors will travel to French side Lyon - who were 31-17 winners over Worcester - in the quarter-finals and, should they progress, they could face Scottish rivals Edinburgh in the semi-finals - they host Bath on Saturday evening for the chance to play Wasps at home in the last eight.