Erin Cuthbert put them ahead in the 23rd minute with a powerful strike from a tight angle 12 yards out.
Melanie Leupolz doubled Chelsea’s lead five minutes later as City could not clear and she scored with a low shot.
City, who won the tournament in 2017, 2019 and 2020, conceded a third in the last minute when Bethany England headed home a Jessie Fleming cross.
The hosts had missed a glorious chance when it was goalless as Ellen White shot just wide and also saw Jess Park have a shot pushed on to the post by Ann-Katrin Berger in injury time.
The second semi-final sees Women’s Super League leaders Arsenal entertain Brighton at Meadow Park (16:45 GMT) in a game you can watch on BBC Two, with coverage beginning at 16:30.
The last final was held in November 2020 behind closed doors at Wembley because of the coronavirus pandemic, but this year’s showpiece – with fans able to attend – will take place at the stadium on Sunday, 5 December.
This competition was delayed by three months earlier in the year because of the pandemic and this was the fifth time in seven years these teams had met at this stage.
However, City, ninth in the Women’s Super League, have had a tough few months, hampered by an injury crisis that includes captain Steph Houghton, reigning Fifa Best Women’s Player Lucy Bronze and goalkeepers Ellie Roebuck and Karen Bardsley among those on the sidelines.
That saw City name only five substitutes, compared to nine from a Chelsea side second in the WSL and who beat Juventus in their Champions League group match last time out.
City started brightly but White, who needs three more goals to be England’s record female goalscorer, could only shoot wide when under pressure.
Chelsea boss Emma Hayes said she “always loved epic games” against City and her side took control after 20 minutes.
Aniek Nouwen headed wide and Fran Kirby was denied by Jill Scott’s excellent goal-saving challenge, before Cuthbert’s fine strike gave the visitors the lead.
Leupolz quickly added the second, but home goalkeeper Karima Taieb should have done better as she was beaten at her near post.
To her credit, Taieb kept City in the game with a number of fine saves to stop Sam Kerr, Kirby at point-blank range, and to deny Cuthbert her second and Chelsea’s third.
Lauren Hemp twice fired wide for the hosts, but Chelsea’s defence remained strong.
England’s late header handed City their biggest home defeat since 2014 and sent Hayes’ side, FA Cup winners in 2015 and 2018, back to Wembley.