Saracens 56-27 Glasgow Warriors
Glasgow scrum-half Ali Price and Saracens full-back Liam Williams both scored in a frantic first five minutes.
Momentum swung Sarries' way after tries from David Strettle and Brad Barritt, before two Adam Hastings penalties reduced the hosts' lead to nine.
But second-half scores for Williams, Strettle, Jamie George and Nick Tompkins sealed the win for Saracens.
Replacement scrum-half George Horne and number eight Matt Fagerson scored consolation tries for Glasgow, whose hopes of reaching the Champions Cup last four for the first time have ended.
Glasgow return to Guinness PRO14 action on Friday night when they host Ulster at Scotstoun.