It is the first time that Emma Hayes' side have ever won a match at the City Football Academy.
The first half was a tight, cagey affair, with the only difference being a scrappy goal minutes before the break.
Both sides had defended well, forcing each other to focus on build-up play to be able to generate chances. However, the number of chances created was minmal and even when they found then, neither side managed to capitalise.
Chelsea had good opportunities within the first ten minutes: first, Bethany England let a cross just fizz past her inside of the box; then Sam Kerr hit the side netting when one-on-one and at a tight angle.
Morgan, on the left of the hosts' defence, played well one again, often doubling up with Lauren Hemp going forwards, and replicated the form shown on Sunday against Aston Villa. In recent matches, she has proved that she is more than capable of playing the same role as that which is usually filled by Demi Stokes.
With minutes left, and no shots on target having been registered in the half, Melanie Leupolz put Chelsea in front. Erin Cuthbert's right-footed free-kick was deflected by a City player and met by the German. Steph Houghton got to her shot on the line, but could not stop it from reaching the back of the net.
One change was made at half time with Laura Coombs joining the sky blues' midfield at the expense of Keira Walsh.
Eight minutes into the second half and the hosts had drawn the scores level. Chelsea captain Magdalena Eriksson dawdled on the ball inside of her box and was dispossed by Chloe Kelly who then rolled a powerful shot underneath Ann-Katrin Berger.
The goalkeeper should probably also take some credit for the mistake, playing a bouncing ball to her centre-back which proved to be difficult for her to control.
It carried on to be a half not too dissimilar to the first, and despite the increased focus on attack from both sides, the best chances were created when their opposition made mistakes.
It was a game in which all of the goals were scrappy; the third was no different. Chloe Kelly swung in a corner, it was cleared but then knocked back in by Esme Morgan. Then, captain Steph Houghton tapped it to Lauren Hemp who shot through a mass of bodies in the box and into the goal.
Niamh Charles, brought in from Liverpool over the summer, had had two shots during her career as a Chelsea player by the end of normal time and had scored both. Just as City thought they had won it, the 21-year-old unleashed a wonderful volley which dipped past Karen Bardsley.
Her goal sidgnalled thirty additional minutes of time on a bitterly cold night in East Manchester.
Five minutes into added time and Chelsea found themselves on top. World-record signing Pernille Harder raced down the right before playing a ball across the box. Bardsley commited to going to ground and parried the ball, but it was met by Guro Reiten who tapped it into the goal while she was still on the ground.
Then, in added time in the first half of extra time, something special from Sophie Ingle made it four for the London club. She was teed up by Guro Reiten around 25 yards out and she swung at it with her left foot, unleashing a rocket which soared into the top-left corner.
Ingle's goal confirmed Chelsea's victory and they now carry on their bid to retain the Conti Cup title
Morgan proves her ability
20-year-old Esme Morgan has increased her involvement at Manchester City this year and the latest changes to the defence have allowed her to feature in the past two matches.
In both Wednesday evening and Sunday afternoon's games, she performed well, either as a full-back or centre-back, and was defensively solid.
Melanie Leupolz joined Chelsea over the summer from Bayern Munich and has quickly become a key part of Emma Hayes' squad.
The Germany international anchored the base of the blues midfield and was regularly influential throughout the match.
Even discounting her contribution with the opening goal of the match, she played a big role in her team's performance on Wednesday night.
Player of the match
It is incredibly difficult to pick a single player who deserves to be named as the best from both sides' performances.
With the two locked in a tight battle for much of the match, it was Chelsea's substitutes who were probably the most impactful.
Guro Reiten scored a goal of her own also set up Ingle for Chelsea's fourth; Niamh Charles added energy in the blues' front line.
Manchester City: Bardsley; Bronze, Houghton, Greenwood (Beckie 59'), Morgan; Walsh (Coombs 45'), Scott, Stanway; Kelly, Hemp, White (Park 105')
Subs unused: Roebuck, Window, Phillips, Ravening, Davies
Chelsea: Berger; Mjelde, Bright, Eriksson, Andersson; Harder, Leupolz, Ji (Ingle 82'), Cuthbert (Reiten 62'); England (Fleming 105'), Kerr (Charles 82')
Subs unused: Telford, Blundell, Kirby, Spence