The South Korea striker fired home from the edge of the box with just six minutes remaining to set up a Final against Notts County at Wembley Stadium on 1 August.
Eniola Aluko could have put Chelsea ahead within two minutes after advancing down the left wing and working her way into the box only for the England international to hit the post.
Chelsea 1-0 Man City
The FA Women's Cup
Monday 4 May
Adams Park, Wycombe Wanderers FC
Nikita Parris then had a chance for City only two minutes later when Toni Duggan and Demi Stokes combined well to find the striker but her shot sailed over the bar.
The pace of the game slowed thereafter before another Parris shot was parried into the path of Natasha Harding, whose effort was blocked by a resolute Chelsea defence just after the break.
Duggan had the chance to put City ahead in the 78th minute but could not get enough connection on Parris’ cross to trouble Blues keeper Hedvig Lindahl.
Then in the 84th minute Chelsea substitute Drew Spence held the ball up well before laying it off to Ji, who scored from 20 yards to settle the contest for the FA WSL 1 leaders.
Chelsea (4-4-1-1): Hedvig Lindahl; Hannah Blundell, Niamh Fahey, Gilly Flaherty, Claire Rafferty; Gemma Davidson, Katie Chapman, Millie Bright, Eniola Aluko; Laura Coombs, Ji So-Yun
Substitutes: Ana Borges for Davidson 73, Drew Spence for Coombs 73, Jackie Groenen for Aluko 87.
Subs not used: Marie Hourihan, Martia Banusic.
Manchester City (4-4-2): Alex Brooks; Lucy Bronze, Steph Houghton, Kathleen Kadtke, Demi Stokes; Natasha Harding, Jennifer Beattie, Chelsea Nightingale, Isobel Christiansen; Nikita Parris, Toni Duggan
Substitutes: Natasha Flint for Nightingale 84, Krystle Johnson for Harding 86.
Subs not used: Karen Bardsley, Emma Lipman, Abbie McManus.
Referee: Adrian Quelch.
Watch highlights of the semi-final game