Both sides had a host of chances to break the deadlock but it took City's Jess Fishlock in the 107th minute to do so.
The Welsh international showed her experience with a well placed volley into the far corner, after Canberra had failed to adequately clear the ball.
City will face Perth Glory in next week's Grand Final, after the Glory smashed Sydney FC 5-1 in the other semi-final.
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