An early goal settled any nerves and, when the Scottish champions went three up with 35 minutes still on the clock, any hope the Belgians had of rescuing the tie disappeared. They had led twice in the 2-2 draw in Liege last week, but apart from a couple of early chances and a late flourish which brought a consolation goal, were rarely at the races on a night when Petershill Park was lashed by incessant rain.
It was City's first Champions League win on their home ground, and their noisy fans enjoyed every minute. Each of the home players, from goalkeeper Lee Alexander out, played their part, but the outstanding player on the park was Welsh captain Jess Fishlock.
Earlier in the day Arsenal had completed their inevitable passage into the last 16 and the focus will now be on next month's showdown between Britain's two most successful clubs. The London side have three Scottish internationalists, as well as coach Shelley Kerr, ensuring intense interest in the tie.
"It's definitely as good a result as we've had in Europe," Wolecki Black said. "We have overcome a very good side and thoroughly deserved the win. A lot of effort went into it and we got a lot of things right. I gave the players a bit of stick after the 2-2 draw last week, but tonight I couldn't fault them. I would rather relax and think about what we did well tonight rather than think about Arsenal right now. That tie will come round soon enough but I can see the Battle of Britain headlines already."
Captain Rachel Corsie added: "We were fired up early on and getting that goal really helped us on our way. We limited them very well and didn't allow the game to stretch, which would have suited them."
Both sides played within themselves in the opening period, but any tension the home side were feeling disappeared with a scrappy opening goal in the 14th minute. A high ball into the visitors' box was contested by Suzanne Mulvey and Aline Zeler, with the striker being credited with sending it past Sabrina Broos.
Although Liege had two chances to equalise, the first hitting a post and the second forcing Alexander to rush out of her box and clear, City the longer the half went on the more City dominated it. Inspired by Fishlock, playing in front of the back four but running tirelessly into dangerous areas, the hosts passed their way through the Belgians in style.
Fishlock forced a good save from Broos after exchanging passes with Suzanne Lappin and firing in a 20-yard shot. The main danger to the home side was trying to play too neatly in front of their own box and Corsie was lucky not to be punished when she gave the ball away to Lewerissa, but the Standard striker failed to take advantage.
Despite this, City deservedly went ahead with a great goal just before the half hour. Fishlock sent in a cross from the right and Denise O'Sullivan volleyed the ball home brilliantly from inside the box. The Republic of Ireland internationalist has not scored too many this season, but this was a valuable one.
Job half done, City nearly made it three two minutes into the second half. An astute pass found Sarah Crilly unmarked on the right edge of the box and when her shot hit the bar, Jo Love's header from the rebound was saved by Broos. Love then lobbed the ball just over the bar after yet another attacking move instigated by Fishlock as the home side continued to press for the third goal which would kill off the tie. It duly arrived in 55 minutes when Crilly's high shot from a similar angle to her earlier one this time found the net.
With the tie in the bag, City eased off and it was the Belgians who had the best chances but Alexander made fine saves from Tessa Wullaert and Faustine Cartegnie. She was beaten eventually, Tessa Wullaert's injury-time effort from close range giving the visitors a crumb of comfort.
City have now beaten the winners and runners-up of last season's BeNe League, emphasising the standards which have been set by this most professional amateur club.