Emma Hunter and Gavin Beith made one change to the starting eleven who kicked off against Celtic last week. Francesca Ogilvie was replaced by Hannah Stewart whilst Nadine Hanssen was in the squad for the first time as she took a place on the bench.
Chances were at a premium in the early stages as the game played out in the middle of the park. The hosts started to get the upper hand but only had a Lauren Davidson shot into the side-netting to show for it from the early exchanges.
Davidson was being utilised in most of City's attacks as she played off the left and her cross from that side just evaded the head of Priscilla Chinchilla at the back post.
Aberdeen then had a half-chance of their own to take the lead. Bayley Hutchison intercepted a pass in midfield and spotting Lee Gibson off her line the Dons striker had an effort from distance which the Scotland keeper did well to get down and hold.
There were signs that the hosts were getting frustrated as both Claire Walsh and Hayley Lauder picked up needless yellow cards before the game was half an hour old.
Glasgow then went close to taking the lead on 28 minutes when Davidson crossed from the left and found Chinchilla but the Costa Rican striker's header went just over the crossbar.
Just two minutes later the hosts went in front and it was almost a carbon copy of the previous chance. Davidson's cross from the left found CHINCHILLA sneaking in at the back post and the striker bundled the ball home for the opening goal.
Aberdeen were more than in the game as the half came to a close with Eilidh Shore in particular standing out in the heart of midfield. The visitors couldn't force an equaliser before the break though as they trailed by a goal to nil at the interval.
The Dons made a double change at half time with Francesca Ogilvie and Mya Christie coming on for Bailley Collins and Hannah Stewart but the half started off with the hosts in the ascendency as Meach saved well from Davidson.
City were pushing hard for a second goal and it arrived just after the hour thanks to a penalty. AJ Meach had come out to challenge Chinchilla for the ball and the referee awarded a penalty as the striker went down in the box. DAVIDSON took the spot-kick and smashed the ball home for 2-0.
Nadine Hanssen came off the bench to make her debut for the Dons with twenty minutes remaining in a rare positive from an afternoon which was about to get worse for the visitors.
Emily WHELAN cut in from the left with 73 minutes on the clock and she sent a powerful shot into the top corner from the angle of the area. The tie was out of sight now for the visitors and it got worse as the game entered the last ten minutes.
Meach did well to tip a Chinchilla drive against the crossbar but the defence switched off as City kept the ball alive and DAVIDSON grabbed her second of the game. Meach and Thomson were replaced by McCann and Greenwood as the Dons made their final changes of the game.
The hosts went on to seal their place in the next round in style as Meikayla MOORE got on the end of Hayley Lauder's free kick to powerfully head home the fifth.