City will play Incheon Red Angels in May, after the South Korean club beat Iran's Bam Khatoon 1-0 in their quarter-final.
The semi-finals and final will be held at an as-yet undetermined centralised venue.
Mariana Speckmaier scored in the fourth minute before a a Blue Whale own goal in the 43rd doubled City's lead.
Holly McNamara won a penalty and converted it in the 63rd minute to decide Sunday's quarter-final in front of 1865 fans at AAMI Park.
The A-League Women leaders will hope star striker McNamara has avoided injury after she came from the field following a knock to her right knee two minutes after her goal.
She had reached for her right knee, but got up and left the field under her own steam.Â
McNamara, who has overcome three knee reconstructions, had been due to be substituted, and appeared in good spirits later in the match.
The home side took the lead when Taylor Otto looped an athletic effort goal bound before Speckmaier made it a certainty by slamming the ball home.
City doubled their lead when McNamara's cross deflected off Li Pei-jung and keeper Tsai Ming-jung could only knock it further into her own net.
In the 63rd minute, McNamara was brought down by goalkeeper Tsai and coolly stepped up to take the penalty herself and converted.
Substitute Emilia Murray won another penalty in the 77th minute but Tsai saved Leticia McKenna's spot-kick.
Taichung came desperately close to scoring when Tanaka's shot slipped through Mieres's open hands and hit the crossbar, only for the City goalkeeper to catch it again.
City, who are aiming to complete a treble this season, face a tight turnaround to play Brisbane Roar at Perry Park on Wednesday, then Wellington away at Porirua Park on Sunday.
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