The Scottish side drew 2-2 with Liege in the first leg in Belgium but were clinical on home soil to seal a 3-1 win.
An Aline Zeler own goal gave the home side into the lead early in the first half before Denise O'Sullivan doubled the advantage before the break with a well-taken volley.
Sarah Crilly drove in a third for City from 18 yards 10 minutes into the second half to end the tie as a contest, meaning Tessa Wullaert's late goal for the visitors was merely a consolation.
Earlier on Thursday, Arsenal booked their place in the last 16 with an 11-1 hammering of CSHVSM-Kairat, meaning they beat the Kazakhstan side 18-2 on aggregate.
After crushing Kairat 7-1 in the first leg in Kazakhstan, Arsenal's progress was all but ensured.
But the Gunners did not ease up at Meadow Park as Danielle Carter grabbed four goals, Kim Little bagged a hat-trick, Jordan Nobbs scored twice and Caroline Weir and Ellen White netted once.
Four of the goals were scored in the first half with most of the damage coming in a 31-minute spell after the break, during which seven goals were added.
Makhliyo Sarikova eventually gave the away side a brief moment of cheer by scoring a consolation goal a minute into added time.