Arsenal reached the last eight after recovering from an early setback to win their 'Battle of Britain' showdown 3-2 on the night, and 6-2 on aggregate.
The Londoners scored the winning goal on the night in second-half injury-time to extinguish the Glasgow challenge.
Suzanne Lappin fired Glasgow ahead after 90 seconds but the lead lasted only nine minutes with Rachel Yankey levelling it to restore Arsenal's three-goal advantage.
That was the way it remained until Jordan Nobbs made it 5-1 on aggregate 21 minutes from time, only for skipper Rachel Corsie to net Glasgow's second on 79.
And, with time running out, Alex Scott completed the scoring deep into injury time.
Birmingham beat their Russian visitors 5-2 on the night - and 7-2 on aggregate.
Birmingham, playing at St Andrews for the time in their history, needed just four minutes to open the scoring through Isobel Christiansen.
Kirsty Linnett scoring the first of her brace against their beleaguered opponents in the tenth minute to make it 4-0 on aggregate.
Zorky levelled matters on the night before the break thanks to goals from Maria Ruiz (29) and Nick Ashley (42).
But any hope of a fightback ended just five minutes into the second half when Kerys Harrop netted Birmingham's third, while Linnett (66) and Melissa Lawley (76) added others.
Other winners on Wednesday were Barcelona and Wolfsburg, with the second legs of the four remaining ties to be completed on Thursday.