Chelsea and England keeper Carly Telford missed today's game for family reasons but is clearly delighted with that result.
ICYMI: How Arsenal beat Everton
Earlier: Everton 1-2 Arsenal
Video content
This content is currently not available
That win for Chelsea means they'll meet Arsenal in 5 May's Wembley final.
Here's a reminder of how the Gunners made it through, with highlights of their win over Everton.
Kirby on match-winning brace
FT: Chelsea 2-0 Man City
Chelsea striker Fran Kirby tells BBC Two: "It's massive for us. We've been preparing for this game for a long time.
"I'm enjoying my football. Luckily for me the ball is hitting the back of the net more often than not.
"The main thing is enjoyment, and I wouldn't be putting the ball in the net if it wasn't for the service."
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Smith on match-winner Kirby
FT: Chelsea 2-0 Man City
Kelly Smith
Former England forward on BBC Two
I would have loved to have played with Fran. She is such a fantastic talent.
'Kirby makes defenders' lives a misery'
FT: Chelsea 2-0 Man City
Sue Smith
Former England forward on BBC Two
Fran Kirby is right up there with the best strikers in Europe. She constantly creates chances and makes defenders lives a misery.
FULL-TIME
Chelsea 2-0 Man City
There it is, Chelsea reach the Women's FA Cup final.
Man City, the holders, are out.
Rex FeaturesCopyright: Rex Features
Post update
Chelsea 2-0 Man City
England's Nikita Parris appears to leave her foot in on Chelsea's Gemma Davison and Eni Aluko is complaining to the officials that it was an attempted stamp.
It certainly wasn't clever from Parris, but it wasn't too malicious either.
YELLOW CARD
Chelsea 2-0 Man City
City's Georgia Stanway is booked for a bad foul on Gemma Davison.
Post update
Chelsea 2-0 Man City
There will be five minutes of added time.
Post update
Chelsea 2-0 Man City
As we enter the final minute of normal time, Chelsea are under no pressure at all and are going to keep their bid to win a treble of trophies this season alive.
Watch: Kirby doubles Chelsea lead
Chelsea 2-0 Man City
Video content
This content is currently not available
Here's how Fran Kirby doubled Chelsea's lead. Super stuff from the England striker.
Post update
Chelsea 2-0 Man City
There's been very little sign of a Man City fightback since that second Chelsea goal.
We're in to the final five minutes of the 90 and the holders are heading out.
Post update
Chelsea 2-0 Man City
Sue Smith
Former England forward on BBC Two
Fran Kirby has been absolutely superb.
Get Involved
#bbcfootball
Tamzin Yates: Fran Kirby is brilliant!!!
DJ Monster: Fran Kirby is good
Catherine Reilly: Excellent second goal for Chelsea versus Man City in women's FA cup semi-final
SUBSTITUTION (Chelsea)
Chelsea 2-0 Man City
Rex FeaturesCopyright: Rex Features
Fran Kirby goes off to a huge ovation after her fine display for Chelsea. She's earned a rest.
On comes Gemma Davison for the fine eight minutes or so.
Post update
Chelsea 2-0 Man City
The crowd at Kingsmeadow watching this one is 3,048.
That's well above average for domestic women's games in England, and the atmosphere has been lively.
SUBSTITUTION (Chelsea)
Chelsea 2-0 Man City
Surely heading for the final now, Chelsea bring on Eni Aluko to replace Scotland youngster Erin Cuthbert.
GOAL: Chelsea 2-0 Man City
Fran Kirby
Video content
This content is currently not available
De. Ja. Vu. Simple goal. On the counter, it's another defensive error from Man City - just like the first goal - and Fran Kirby shows her class to race clear, cut inside and finish past the keeper. Quality finishing. It's almost an exact replica of the opener.
Live Reporting
Tom Garry
All times stated are UK
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Latest PostA London derby at Wembley
FT: Chelsea 2-0 Man City
Video content
So, Arsenal and Chelsea will contest the 2018 Women's FA Cup final at Wembley on Saturday, 5 May.
Thanks for your company on BBC Sport this afternoon for the semi-finals. It's been a pleasure.
Until next time, good bye!
Hayes on 'gutsy' Chelsea
FT: Chelsea 2-0 Man City
Chelsea boss Emma Hayes tells BBC Two: "It was a gutsy performance.
"To get that second goal at that time in the game was important.
"We took our chances but, defensively, we were absolutely superb today. Every squad player pulled together."
Telford's joy
FT: Chelsea 2-0 Man City
Chelsea and England keeper Carly Telford missed today's game for family reasons but is clearly delighted with that result.
ICYMI: How Arsenal beat Everton
Earlier: Everton 1-2 Arsenal
Video content
That win for Chelsea means they'll meet Arsenal in 5 May's Wembley final.
Here's a reminder of how the Gunners made it through, with highlights of their win over Everton.
Kirby on match-winning brace
FT: Chelsea 2-0 Man City
Chelsea striker Fran Kirby tells BBC Two: "It's massive for us. We've been preparing for this game for a long time.
"I'm enjoying my football. Luckily for me the ball is hitting the back of the net more often than not.
"The main thing is enjoyment, and I wouldn't be putting the ball in the net if it wasn't for the service."
Smith on match-winner Kirby
FT: Chelsea 2-0 Man City
Kelly Smith
Former England forward on BBC Two
I would have loved to have played with Fran. She is such a fantastic talent.
'Kirby makes defenders' lives a misery'
FT: Chelsea 2-0 Man City
Sue Smith
Former England forward on BBC Two
Fran Kirby is right up there with the best strikers in Europe. She constantly creates chances and makes defenders lives a misery.
FULL-TIME
Chelsea 2-0 Man City
There it is, Chelsea reach the Women's FA Cup final.
Man City, the holders, are out.
Post update
Chelsea 2-0 Man City
England's Nikita Parris appears to leave her foot in on Chelsea's Gemma Davison and Eni Aluko is complaining to the officials that it was an attempted stamp.
It certainly wasn't clever from Parris, but it wasn't too malicious either.
YELLOW CARD
Chelsea 2-0 Man City
City's Georgia Stanway is booked for a bad foul on Gemma Davison.
Post update
Chelsea 2-0 Man City
There will be five minutes of added time.
Post update
Chelsea 2-0 Man City
As we enter the final minute of normal time, Chelsea are under no pressure at all and are going to keep their bid to win a treble of trophies this season alive.
Watch: Kirby doubles Chelsea lead
Chelsea 2-0 Man City
Video content
Here's how Fran Kirby doubled Chelsea's lead. Super stuff from the England striker.
Post update
Chelsea 2-0 Man City
There's been very little sign of a Man City fightback since that second Chelsea goal.
We're in to the final five minutes of the 90 and the holders are heading out.
Post update
Chelsea 2-0 Man City
Sue Smith
Former England forward on BBC Two
Fran Kirby has been absolutely superb.
Get Involved
#bbcfootball
Tamzin Yates: Fran Kirby is brilliant!!!
DJ Monster: Fran Kirby is good
Catherine Reilly: Excellent second goal for Chelsea versus Man City in women's FA cup semi-final
SUBSTITUTION (Chelsea)
Chelsea 2-0 Man City
Fran Kirby goes off to a huge ovation after her fine display for Chelsea. She's earned a rest.
On comes Gemma Davison for the fine eight minutes or so.
Post update
Chelsea 2-0 Man City
The crowd at Kingsmeadow watching this one is 3,048.
That's well above average for domestic women's games in England, and the atmosphere has been lively.
SUBSTITUTION (Chelsea)
Chelsea 2-0 Man City
Surely heading for the final now, Chelsea bring on Eni Aluko to replace Scotland youngster Erin Cuthbert.
GOAL: Chelsea 2-0 Man City
Fran Kirby
Video content
De. Ja. Vu. Simple goal. On the counter, it's another defensive error from Man City - just like the first goal - and Fran Kirby shows her class to race clear, cut inside and finish past the keeper. Quality finishing. It's almost an exact replica of the opener.