Jen Beattie grabbed the winner from close range with just over ten minutes remaining to send the City fans wild and seal a place against Birmingham City Ladies in the final.
Nick Cushing made one change to the side that beat Reading Women last weekend with Marie Hourihan replacing Karen Bardsley in goal.
It was a close encounter between the two sides in the first half as both looked to get a foothold on the game and grab the opening goal.
City’s first chance of the game came about in the 18th minute when Jill Scott knocked the ball down to Jane Ross, who saw her hooked shot deflected just past Emma Byrne’s post.
Hourihan was rarely tested in the first 45 minutes at the Academy Stadium but she showed great awareness midway through the half to smother the danger at the feet of Asisat Oshoala.
The two were involved in the action minutes later as Oshoala beat Hourihan to the ball before sending a lob way off target.
As the first half came to a close, both sides created good chances to take the lead.
First, Danielle Van De Donk fired over Hourihan’s crossbar from ten yards out before Scott picked out Nikita Parris, who couldn’t get a clean connection on the ball and saw her effort trickle narrowly wide.
The second half had a similar start to the first with neither side allowing good goalscoring opportunities to score.
Carter and Houghton created room for themselves at either end of the pitch but didn’t trouble the respective goalkeepers.
The City skipper and Lucy Bronze then combined in their own area to prevent Carter’s low shot troubling Hourihan as the game ticked into the 57th minut
The Blues shot stopper pulled off the save of the game 18 minutes later when she denied Oshoala from close range before Carter fired over the rebound from six yards under pressure from Bronze.
Four minutes later, City broke the deadlock to secure the win. The ball rebounded in the box and fell at the feet of Beattie, who slammed home from close range.
The Gunners had a great chance to level with five minutes remaining but Houghton came to the rescue with a block that booked the Blues their final berth.
