City, who are top of the Women's Super League, won the League Cup after beating Arsenal in the final last month.
Chelsea clinched a semi-final spot for a sixth consecutive season with a hard-fought 1-0 win over part-time side Durham.
Rakel Honnudottir's last-gasp goal helped Reading beat Manchester United 3-2 after extra-time, while West Ham edged past Championship side Aston Villa 1-0.
Reading and City will host the semi-final ties on April 14, with the final scheduled for May 4 at Wembley Stadium.
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford/Amlan Chakraborty)
