Chelsea's bid for a quadruple continues, but it looked in doubt at times on a cold afternoon.
They were gifted an early opener as Catarina Macario cut through City's defence before playing Ramirez through on goal.
The Colombia striker's initial shot was saved by Ayaka Yamashita, but it deflected back off Aleixandri and into the path of Ramirez for a simple tap-in.
Chelsea's winner also came down to an unfortunate error from City, with a well-worn pitch wreaking havoc as the ball bobbled up before Hasegawa turned Ramirez's low cross into her own net.
The Chelsea players' celebrations were muted at the final whistle, with Bompastor's side breathing a sigh of relief, knowing the performance was a far cry from their best showings this season.
"As you can see, the performance was maybe not a great one but we found a way to win the game," Bompastor said.
"The performance was good enough for us to win. We created some chances and scored two goals, which is a lot in a final, especially when you play City. I know this team has more than what we showed today."
But as the dust settled and they collected their medals, the players danced joyfully with the trophy in front of their fans.
The celebrations will be short lived, however, with focus shifting to their next three encounters against Cushing's side.
"When you are at these big clubs, the pressure is on results so when you win you are able to celebrate. These are the moments you want to enjoy with players, staff and fans," Bompastor added.
"Every game they make an effort to come so when you have an opportunity to give happiness with trophies, that is the best thing you can do."
Fara Williams
