City, aiming to lift the League Cup trophy for a third time after triumphs in 2014 and 2016, took control of the game in the second half as Parris scored a penalty in the 49th minute before adding another nine minutes from time.
They face Arsenal or Manchester United -- who play in Thursday's second semi -- in the final on Feb. 23, a day before the men's team meet Chelsea in the League Cup final.
(This story has been refiled to 'Wednesday' in first paragraph)
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford)
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